In London, American heiress Kit Preston (Doris Day) has been married for three months to a British executive, Anthony 'Tony' Preston (Sir Rex Harrison). During a foggy evening while walking across Hyde Park, Kit is threatened by a voice that tells she will be murdered soon. The next day, Kit receives a phone call from the stalker threatening to kill her in the next month. She and her husband go to Scotland Yard, but Inspector Byrnes (John Williams) believes that Kit may be making up the story to get more attention from her husband. Kit's Aunt Bea (Myrna Loy) arrives, but only Kit receives the phone call raising the question: is she losing her mind?