Dirk Gently meets with a new client and explains that his methods of deduction relate to the interconnectedness of all things, and that he has an essential list of expenses. The client, elderly Ruth Jordan, doesn't care as long as it helps him find and return Henry. Dirk assures her that's what he does, and asks her for a photograph... of her cat, wearing a pope's hat.
Outside, a relieved Dirk kisses her check and then hears the sound of breaking glass from a nearby flat. He goes to investigate and sees a man breaking in through the back door. Dirk calls Ruth for the neighbor's telephone number, and then calls the number. When the answering machine of the occupant, Susan Harmison, picks up, Dirk tells the thief to answer. When he does, Dirk addresses him by name as Richard MacDuff and tells him to take better precautions. Richard has no idea who he's talking to, and Dirk tells him to come to the window. When Richard does, Dirk takes his picture and tells him never to show his face at the window. When he recovers his sight, Richard looks out again and recognizes Dirk from university when they were students together. He goes out and insists that he lives there, and that he was just taking the laptop so he could hack into her account before she read the angry letter he wrote her. Dirk offers Richard his card: Dirk Gently: Holistic Detective Agency. When he explains that he's looking for a cat, Richard suggests that he check out the nearby warehouse.
Dirk goes to the warehouse to investigate and Richard accompanies him. As he picks the lock, Dirk comments that their meeting will be more significant than they can imagine. They go inside and find a set of cat prints and banks of electronic equipment. Dirk finds a single rose petal on the floor next to a metal grid, and they carefully step around it. Examining the equipment, Dirk finally presses a keyboard and a warning flashes, saying that it's the incorrect code and the station will explode in twenty seconds. While Richard panics, Dirk looks around, insisting that it's a bluff... until he finds several pounds of plastic explosives. They run out of the warehouse just in time.
The next morning, the police cordon off the warehouse while Richard is at home cleaning up the broken from the window he broke to get in. Susan is watching a broadcast about the explosion, and the death of CEO WayForward Technologies Gordon Way. DI Gilks says that he's launching a missing persons inquiry as there's no sign of a body in the debris. Susan then tells Richard that he can do whatever he wants as long as it makes him happy, but whatever he's doing isn't succeeding. She leaves for her job as a doctor and then tries to call Gordon, but gets his answering machine. As she leaves a message asking why he was in a warehouse on her street, Miss Jordan comes out and asks if she heard the explosion. Susan admits that she was out the previous night, and Miss Jordan tells her that she hired a detective to find her missing cat.
Richard goes to Dirk's office and finds a seedy building and an overworked receptionist, Janice Pearce. She tells Richard that she's leaving because she hasn't been paid, and then storms out. Richard goes into Dirk's office and discovers that he's wearing a painter's coverall and is covered in white paint. He tells Dirk that his receptionist has quit, and notes that he had heard that Dirk was kicked out of the university for cheating. Dirk denies it and starts painting over his whiteboard, and then explains that he uses chaotic methods to solve cases, by investigating the interconnectedness of all things. He insists that it works, and notes that Richard is there with Susan's laptop and needs Dirk's help to hack the e-mail. As they go, they discover that the receptionist is back. She explains she came back so Dirk would notice when she quits for good.
Outside, deliverymen bring Dirk's new fridge, and he explains to Richard that his cleaner has padlocked the one at his flat. They go to Dirk's beaten-up old car, the Princess, and Richard realizes it's the same one he drove at university. Dirk's unable to get it started, and they proceed on foot. As they walk, Dirk explains that he became a private detective when he was called in to investigate the disappearance of Schrödinger's Cat, Bernice, and it decided to escape because it was tired of being locked up in a box. Dirk then goes to a schoolyard and pays a 10-year-old schoolboy to hack the account. While the boy works, they go to the local store and Dirk buys 200 cheap cigarettes. When he discovers he's left his wallet at the office, he has Richard pay for it along with a newspaper. Outside, Dirk confirms that the warehouse belonged to the missing Gordon Way, whose car was parked outside. Now they know that Gordon wasn't there, but Dirk figures they shouldn't talk to the police.
Back at the schoolyard, Dirk pays off the boy with the cigarettes. Richard confirms that Susan hasn't read his e-mail yet, and notices an e-mail from Gordon Way. He's surprised to learn that Susan knows Gordon, and Dirk insists that it's all part of a related web of events that will lead to the missing cat. Richard doesn't want to get involved, but Dirk warns that he's already involved, and figures that he wants to know Gordon's connection to Susan. The newspaper article reports that a Dr. Gerstenberger was the last person to see Gordon, and they need to track him down. Dirk looks up his address and they go to his office.
As they arrive at Gerstenberger's office, Dirk suggests that there's a connection between Henry the Cat and Gordon the CEO. When Dirk sees the waiting room and realizes that Gerstenberger is a therapist, he immediately goes outside and tells Richard to lie on the grass. Richard refuses until Dirk explains that Gordon was seeing a therapist, and figures that they need to see Gerstenberger's files. Richard still doesn't understand why he has to lie on the grass, but Dirk insists it's critical to learning the connection between Susan and Howard. Richard does so, positioning himself as Dirk specifies. Dirk then bursts into Gerstenberger's office and starts ranting. Gerstenberger tries to calm Dirk down, but he runs to the balcony and apparently leaps. The doctor looks down and sees Richard at a distance, and mistakes him for Dirk. As he runs downstairs, Dirk emerges from hiding and goes through Gerstenberger's files, then slips out as the doctor discovers that Richard isn't Dirk.
As they drive, Dirk goes over the files and discovers that they reveal that Gordon was obsessed with Susan after they met at university, and met her at a hotel a week ago. Shocked, Richard brakes to a halt and Dirk suggests that they go to a bar, where he buys several drinks. He tells Richard that Susan must be lying to him, and offers to talk to her. When Richard refuses, Dirk leaves him with the tab and goes to run some errands.
Dirk goes to Susan's office where she works as a doctor, pretends to recognize her, and points out that they went to university together. He complains about his shoulder, but she tells him to take off his clothes so she can do a prostate exam. He reluctantly does so, but Susan relents and tells him that she knows that Miss Jordan hired him to find her cat. As he puts her pants on, Susan says that she doesn't have time for his bullshit,. but he says that he wants to talk about Gordon. They go for a walk and Dirk asks her if she ever saw Gordon with Henry. She doesn't understand the connection, but admits that a week ago, Gordon asked her to marry him. He's been doing it for years, and she has always told him that they have no chance after he was gone the night Susan told him to be at his house for her birthday. Gordon was always obsessed with computers, and he promised to be there but failed. He told Susan that he was hit by a car on the way, and she didn't believe him. Dirk takes down the exact date of the incident, December 5, 1994, and that they were to meet at her parents' house. He points out that their address is right next door to the warehouse, and confirms that she didn't know Gordon owned the warehouse.
Next, Dirk returns to see Miss Jordan for more tea. He notes that there's a photo of her and her cat, and she explains that the cat is Henry's predecessor, George. She has vowed never to get another cat, but couldn't resist when she saw Henry. He notices that she's taking medication, and makes sure that she'll be okay long enough to pay her bills. He then asks her how she met George, and Miss Jordan says that George came running into her house one day. She never did find his owner, and she kept the cat until 2006 when he died. he's now buried beneath the rose garden in the back yard. Dirk has her confirm the date, and as she flips through her photo album, he notices her with a man. Miss Jordan says that it was her husband, Harry, who walked out on her never to be seen again. She finally confirms that Henry entered her life on December 5, 1994, and Dirk realizes that it's the same date that Susan and Gordon split up. He asks if Miss Jordan ever saw Gordon entering the warehouse, and she quickly denies it. Miss Jordan asks how Gordon was connected to Susan. Dirk obligingly explains and pockets her cookies.
Richard confronts Susan about Gordon, and she admits that she saw him recently. However, she says that they had coffee and nothing else, and needs a reason for her and Richard to be together. Richard tells her about the e-mail he sent her, and Susan asks him to go.
Dirk is going over his notes in his car when DI Gilks comes by and demands to know why he's there. He isn't interested in hearing about holistic theory. Dirk then goes back to his office and tries to put all of the pieces together. Richard comes in and admits that he broke up with Susan over her affair. However, Dirk assures him that he checked out Susan's story, and in fact she rejected all of Gordon's advances. Dejected, Richard says that he's an out-of-work screw-up after he was let go from his job as a business analyst at a power company. After making sure that Richard can still pay his bills, Dirk reexamines the case and realizes that Richard is the common thread. He asks permission to hypnotize Richard, who reluctantly agrees. They proceed and Dirk puts Richard into a trance. He then regresses Richard back to December 5, 1994, and Richard remembers shouting at Dirk, who claimed he was clairvoyant and could predict all the questions in the exam. He charged Richard but failed, and when Richard chased him to get his money, Dirk backed his car into Gordon Way. Gordon was carrying flowers, and Dirk figures that he was going to see Susan. Going back to the board, Dirk tries to figure out the connection between George appearing and Mr. Jordan disappearing. He then suggests that Richard come into business with him. Thanks to a post-hypnotic suggestion that Dirk planted, Richard considers it. Dirk tells him to get some backbone and call Susan.
Susan takes Richard's call, and he asks her about Mr. Jordan. She agrees to see Miss Jordan and get her to call Dirk with the information, and wonders if that's all that Richard wants. He says it is and hangs up, and explains that Susan is going to see Miss Jordan. Dirk tells him that Susan is in grave danger and they try to drive over, only for the car to stall.
Susan shares her woes with Miss Jordan, and then tells the old woman that Dirk was asking about Harry. When Miss Jordan hears that, she grounds up more of her medication and pours tea. As Susan drinks her tea, Miss Jordan asks her about Gordon and stares intently. Susan wonders if something is wrong, and the doorbell rings. She goes to get the door and finds Richard and Dirk there. They're surprised to see that Susan is alive, and they see Miss Jordan inside. Dirk tells her that he's found Henry. As they settle down for tea, Dirk explains that in 1994, Gordon hurried to meet with Susan, but Dirk backed over him. When he lost Susan, Gordon set out to build a time machine and go back in time to change things. Susan thinks that Dirk is insane, but Dirk continues and says that on the day of his disappearance, Gordon was going to go back in time. However, Henry entered the warehouse and got onto the platform, and went back into time with Gordon. The only thing left was the rose petal from the flowers that Gordon took with him. When Henry reappeared in 1994, he went home to Miss Jordan, and she renamed him George. Miss Jordan admits that they were the same cat, and now George/Henry is buried in the back yard after 14 happy years with his mistress.
Susan thinks that Dirk is making up a con story, but Miss Jordan believes Dirk and goes to get her check book. As she does, Dirk casually asks her why she killed her husband. Miss Jordan cheerfully admits that Mr. Jordan was an abusive unpleasant bastard. He went too far when he abused George/Henry. She beat him dead with a frying pan. At the same time, Gordon had completed his trip through time and left for Susan's house. When he walked by Miss Jordan's house, he saw Harry's dead body and Miss Jordan killed him.
Miss Jordan admits to everything, even when Susan points out that it's impossible. However, the old woman says that they have no evidence against her, and it doesn't matter. She poisoned all of their teas. They get into Dirk's car and it starts up. As they drive to the hospital, Richard apologizes to Susan for his lack of confidence, and promises that he'll change his life. As they kiss, Dirk calls DI Gilks and tells him that he's been poisoned. They arrive at the hospital ER, but the doctor informs them that there was no trace of poison.
The trio returns to Miss Jordan's house, where the police have already secured the area. DI Gilks lets them in and they discover that Miss Jordan killed herself with an overdose of her own medication. Gilks demands an explanation, and Susan blames Dirk for telling her that Henry wasn't coming back. She slaps him and walks out, and Richard goes with her. Dirk asks Gilks if Miss Jordan left him a check, and the detective inspector orders him out.
Five days later, Richard is wearing a suit and says he has a new job. He's invested his $20,000 into Dirk's agency, but Susan points out that Dirk hypnotized him right before he decided it was a good idea. She tells him that it’s his money, and leaves to sort out Miss Jordan's apartment. Richard calls Janice to find Dirk, and tells him that Dirk is out in the country.
As Susan packs Miss Jordan's things, she finds Gordon's phone. She plays back the voicemail that she left him earlier, and then finds a newspaper from 1994. Susan realizes that everything that Dirk said was true.
Richard tries to reach Dirk at a hotel. Dirk is busy enjoying a drink by the pool when he gets Richard's call. Richard asks for the money back, but Dirk tells him that he spent all the money on expenses for a new case... that has taken him to Barbados.