Dr. Jeff Cameron, Robert Mitchum, treats a troubled attempted suicide victim. The patient signs herself out, then sends a telegram inviting him to meet her at a mansion. He breaks a date with his nurse girlfriend Julie Dorn, Maureen O'Sullivan, because he fears Margo may try to harm herself again.
The doctor grows fond of Margo Lannington, Faith Domergue, and they begin seeing one another. Told she is flying to Nassau with her aged father the next day, a tipsy Jeff shows up unannounced and bluntly tells Frederick Lannington, Claude Rains, that he is in love with his daughter. Lannington reveals that Margo is his wife. Jeff leaves, dazed, but returns when he hears a scream and finds Margo clutching an earring torn from her ear. Jeff agrees to get involved in the domestic trouble. Lannington strikes him with a fireplace poker; in the ensuing struggle, Lannington is knocked down, hits his head on the floor and lies unconscious. Dazed, Jeff goes to the bathroom; when he returns, the man is dead.
Jeff wants to call the police, but Margo persuades him that they would call it murder if they panic. Seizing the moment, she exploits Jeff's concussion and naiveté to urge them to run away together. They first attempt to use airline tickets but spot policemen; they then decide to drive to Mexico, swapping Margo's convertible for a pickup from a roguish used-car dealer. Jeff's condition worsens, his headaches and fog turning into a warning that paralysis could follow.
In Postville, Arizona, they are brought before the sheriff, but only because Jeff is not wearing a beard for the town's "Wild West Whiskers Week." When Margo claims they are bound for Mexico to marry, the police chief insists they marry in town. Their honeymoon finds a radio broadcast exposing Margo's psychiatric treatment. They slip away, but the border patrol is alerted after the chief identifies Margo in a photo. It emerges that Lannington was smothered to death with a pillow.
In a border town, the fugitives pawn Margo's bracelet for extra cash, then turn to theater owner Milo DeLong, Philip Van Zandt, who offers to smuggle them into Mexico for $1,000. Jeff's left side grows paralyzed; he realizes that Margo is mentally unstable and is the killer of her husband, and he resolves not to finish the trip. When he tries to stop Margo from leaving, she knocks him down and then smothers him, though he remains alive long enough to drag himself to the border. Margo sees him arrive and fires; the police return fire, killing her. The police initially treat Jeff as an accomplice, but before she dies she proclaims that she acted alone, and that Jeff "didn't even have sense enough to know."
While recovering in the hospital, Jeff asks the doctor, > Can I send flowers to San Francisco?
The doctor replies, > I think so, and steps into the hall to fetch Julie.