Bill Templeton, John Beck, and his wife Janice Templeton, Marsha Mason, live a privileged life in Manhattan's Upper West Side with their 11-year-old daughter Ivy, Susan Swift. They begin to notice a stranger shadowing them in public places and grow alarmed when the man follows Janice and Ivy home one afternoon. The man reveals himself as Elliot Hoover, Anthony Hopkins, a widower who lost his wife and daughter, Audrey Rose, in a car accident in Pittsburgh. The couple agree to have dinner with Elliot, during which he explains that he believes Ivy is a reincarnation of Audrey, and that psychics confirmed his suspicions; he learned from them intimate knowledge of the couple's apartment and that Ivy was born minutes after Audrey died.
Bill believes Elliot is extorting the family. He invites Elliot to their apartment, and arranges for his attorney friend, Russ Rothman, Stephen Pearlman, to listen covertly from upstairs. When Elliot speaks Audrey's name, Ivy enters a state of panic, which is only calmed by Elliot's presence. In this state, she bangs her hands against the cold window, and it leaves inexplicable burns. Elliot comforts her, after which she recognizes him as "Daddy" and falls asleep. Elliot insists that Ivy's burns are evidence of her reincarnation, as Audrey burned to death in the car accident. Bill grows enraged by Elliot and forces him out, punching him, but Janice and even Russ are sympathetic to the strange man's plea.
One night while Bill is working late, Ivy experiences another night terror, in which she thrashes around violently. Janice is surprised by Elliot's appearance at her door and allows him in to help calm Ivy. During Ivy's next episode, Bill attacks him. After a struggle, Elliot locks the couple out of their apartment and disappears with Ivy through a service exit. An attendant informs them that Elliot rented an apartment in the building. Police discover him and Ivy in the apartment and charge him with child abduction.
A trial ensues, during which Janice and Ivy have Ivy sent to a Catholic boarding school in upstate New York to shield her from the public. Elliot attempts to persuade the jury that his actions were necessary to grant peace to Audrey's spirit. The trial becomes an international news story, with a Hindu holy man testifying about their religious belief in reincarnation. On the stand, Janice admits that she believes Elliot. The judge grants a recess in the trial, and Janice and Bill are informed that Ivy has injured herself at her school by crawling toward a fire pit during a Christmas celebration.
After Ivy is treated for burns, Janice remains in upstate New York in a hotel. In the middle of the night, Janice finds Ivy repeatedly greeting herself as Audrey Rose in the mirror. In a motion to complete Elliot's trial, Bill and Janice's attorney requests that Ivy be hypnotized as a means of proving she is not a reincarnation of Audrey. The hypnotist employs a past life regression hypnosis, which is observed in a hospital by the jury. Ivy revisits the traumatic car crash that took Audrey's life and reacts violently. She loses consciousness, and Elliot scrambles in to attempt to calm her but she dies in his arms.
Sometime later, Janice writes a letter to Elliot, thanking him for transporting Ivy's cremated remains to India, and expressing her hope that Bill will come to accept her and Elliot's belief that Ivy was a reincarnation of Audrey. A closing intertitle quotes the Bhagavad-Gita.
