In San Francisco, concert pianist Erik Sutton goes to the police station and asks Sgt. Joe Brice for a report on his stolen car. Brice is curious to know why Erik came in at 5 a.m. to check, and Erik says that he was up early practicing. The detective also wonders why when his car was stolen, Erik was up a 2.a.m. The pianist says that he was out at liquor store, but Brice points out that liquor stores aren't open at that time of the morning. He assures Erik that they'll find his car, but the pianist is more interested in the hitchhiker that he picked up, the woman who stole his car.
A week later, Erik returns to the station and Brice wonders why he's there, given that they found and returned his car three days ago. Erik tells him that the same woman stole his car again when he parked it to go for a walk. Brice wonders if the mysterious woman has some connection to Erik, possibly a mistress, and the pianist explains that he and his wife are separated, and she never met the woman. Erik doesn't recognize the woman from mug shots, but works with a sketch artist to produce a drawing.
A motorcycle policeman gives a ticket to a limo and the owner, Claire Foster, comes out. The policeman recognizes her from the sketch and invites her down to the station. Brice calls Erik in and explains that Claire is married to a rich architect, Walter Foster. She says that she was with him at both times that Erik says his car was robbed, but that her husband left for Venezuela on a job and can't confirm her alibi. They have Erik check a lineup of women, including Claire, but he claims not to recognize her. The pianist leaves and Brice apologizes to Claire, explaining the situation. The detective receives a report from the lab confirming that Erik's fingerprints were the only ones in the car, and he orders his men to bring the pianist back. Claire tells Brice that she won't press charges but wants to talk to Erik.
Erik has gone to a bar to drink and Claire tracks him down. He finally tells her that she's the woman that he's been dreaming about ever since college, even though they've never met. Claire insists that it's a coincidence, but Erik tells her that it was her image in his mind that let him get through all of his personal problems in the last few months. He finally tried to find her by hiring a detective agency, but they had nowhere to start. That was when Erik went to the police and made up the car theft incidents, knowing the police would try and track down Claire and find her for him. Claire says that he went to a great deal of effort to find "her," rather than "the woman," and Erik realizes that she has accepted her story. However, Claire insists that she's never dreamed of him and that she's happily married
When Erik persists, asking if she's happy in her marriage, Claire tells him to drop it and suggests that he see a psychiatrist. She notes that Walter is seeing a psychiatrist because he dreams of a man with a scar on his right hand strangling him in his sleep. She embraces him and they kiss, and then Claire checks Erik's hand and determines that he doesn't have a scar. She admits that she had hoped it would be Erik so that he could kill her husband and free her. Walter won't give her a divorce and if she fights it in court, she'll lose. Erik invites her to come with him on his tour, but she says that she can't. She asks him to stay with him but he says he can't because of his concert commitments. When he tells her that, Claire embraces him, and then takes a pair of scissors from her purse and slashes Erik's right hand. As he stares at the wound in horror, Claire tells him that he can stay with her until the stiches are ready to be taken out, and that everything will work out perfectly.