Oliver Brandt and Bertie Hastings are business partners with some very rich clients. Hastings discovers that Brandt has been using creative accounting to embezzle funds from their clients' accounts.
The partners are also members of The Sigma Society, a Mensa-like organization for people with IQs in the top 2% of the population. During a meeting of the society, Hastings takes Brandt aside into an upstairs office and tells him he intends to go public with the facts on Brandt's thefts. Brandt, however, anticipated the confrontation and set up an ingenious method for murdering Hastings while providing himself with a cast-iron alibi.
Before his meeting with Hastings, Brandt had set up a programmable turntable so that when it finishes playing a record, the cue arm makes electrical contact with two posts on the turntable, which will set off firecrackers to simulate the sound of gunfire. Brandt then shoots Hastings using a silenced gun, starts the turntable playing and returns to the Sigma Society meeting downstairs. A few minutes later the sounds of "gunshots" are heard upstairs and as everyone rushes up to investigate, Brandt dismantles his rigged turntable during the confusion.
Everything seems to be going according to plan until Columbo uses Brandt's own intelligence and ego against him, and he makes a slip that demonstrates his guilt.
Watch for an 18-year-old Jamie Lee Curtis as a surly waitress as well.