Enough Rope

Psychologist Robert Flemming wants to be rid of his wife, but his solution is not divorce. Instead, he seduces a young patient, Susan, and convinces her to join him in a conspiracy to kill his wife, so Susan can be with him. Flemming arranges for him and his wife to fly to Toronto. As they are ready to leave for the airport, Flemming strangles his wife, leaves her body in their apartment, and he and Susan go to the airport, with Susan impersonating his wife. Just before the plane is about to take off, they stage an argument and Susan storms off, leaving him to fly to Toronto alone. When the wife's body is discovered in the apartment, Flemming has what looks like an airtight alibi -- his wife was seen alive on the plane, and he was in Toronto when the body was discovered. It is the perfect murder -- until Lieutenant Columbo starts investigating. The first appearance of the legendary detective (cigar and all).