Millicent Hardy returns to the home that she shares with her twin sister, Marion, who runs a dance studio upstairs while Millicent runs the antique store downstairs. As she unlocks the door, Millicent notices that the mail and milk haven’t been picked up in several days. Going inside, Millicent discovers that the house is a mess and the cat hasn’t been fed. As she checks the house, Millicent hears music and the sound of tap shoes from the studio. Going upstairs, she finds her sister Marion... hanging by her neck from the rafters.
Six weeks later, Millicent refuses to reopen the shop. A local land developer, William Jason, tries to get hold of her by phone without success and sends her friend Sam Davis. Meanwhile, a local boy comes to see Millicent if she’ll be opening the store again, but she say she won’t for a little while. Millicent then goes to find the cat and discovers him in the bedroom. Looking into the darkened room, she sees what appears to be her sister, screams, and faints. Sam arrives and wakes her, and shows her that the “head” was a wig dummy’s head. He wonders why Millicent is still torturing herself over Marion’s death, and she shows him all the things around the house that belonged to Marion and keep appearing. Sam insists that she is suffering from guilt, blaming herself for being gone when Marion killed herself. He suggests that she talk to a psychiatrist, and then says that William wants to buy the property. Millicent refuses to hear of it and tells him to leave, and then lights up one of Marion’s cigarettes... even though she doesn’t smoke.
After Sam leaves, Millicent hears music coming from the studio. There is no one there, and Millicent calls out to her sister, asking her to leave her alone and apologizing for not being there.
Later, William comes to see Millicent and make an offer on the property. Millicent is distracted when she hears the music and tap-shoes, but William says that he doesn’t hear anything. He offers a swap for a similar home that he owns and $8,000 as well, and suggests she could be free there of her sister’s memory. Millicent says that twins are never free of each other and then starts upstairs, only to stop when William leaves and slams the door. The phone rings and Millicent reaches for it, and sees her sister’s locket on the desk. Inside of it is a drawing of a skull. When she answers the phone, she discovers that it’s Sam’s psychiatrist, Dr. Coolidge, and Millicent begs him for help.
Millicent shows Coolidge the locket and insists that she buried it with Marion. He suggests that there’s a part of her mind that is doing everything and making her forget. Coolidge says that it isn’t Millicent’s fault, and finally explains that Marion was with a number of men, including several married ones. Millicent asks for a cigarette and Coolidge points out that she doesn’t smoke, and then suggests he see a colleague in Boston. Millicent starts talking about herself as if she were a different person, Marion, and quickly leaves.
Back at the house, Millicent gets out of the cab and sees a figure hanging in the studio. When she turns back around, it has vanished. Inside, Millicent prepares for bed when she hears a door slam and a banging noise. When she checks it out, Millicent discovers that the front door is unlatched. She fastens it and finds another of her sister’s cigarette butts in an ashtray. Millicent asks her sister what she wants but gets no answer, and starts to call Sam. Before the call can go through, Millicent hears the same noises from the studio.
Nerving herself, Millicent goes to the studio dressing room, hearing her sister calling to her. Inside is a tap-dancing costume. Millicent puts it on and goes into the studio, and finds a noose waiting for her. When she refuses to hang herself, a man moves out of the shadows and says that he’ll help her. It’s William, who explains that Marion was blackmailing him. He wanted to buy the building so he could find the letters he sent to Marion and burn them. As he starts to strangle her, Millicent says that she knows where the letters are hidden. She goes to the piano and removes them. As William confirms that they’re all there, Millicent says that this time she’s ready for him, and then takes revolver out of the piano and shoots him dead.
Later, the medics take William’s body away, while the police confirm that the developer had hidden speakers throughout the house. Once they leave, Sam explains that William was backed by his family, who would have withdrawn their support if word of the affair got out. However, Millicent asks how she could have known where the letters and revolver were hidden... and hears the sound of her sister’s tap-dance shoes from above.
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