Audrey Rose
(1977)

Bill and Janice (Marsha Mason) Templeton have a daughter named Ivy. They notice a strange man stalking the family.  The man, Mr Hoover (Anthony Hopkins), believes that Ivy Templeton is the reincarnation of his dead daughter Audrey Rose. The parents think he is crazy, but when Mr Hoover says the name Audrey Rose, the girl goes into a trance. Hoover rents an apartment in their building, and continues trying to convince them it is his daughter.

Months later, Hoover is on trial for kidnapping the girl. During the trial, Ivy is hypnotized to prove that Hoover's story is false. Under hypnosis, she relives the car crash where Audrey Rose died. Ivy really was Audrey Rose, but she dies again from reliving the trauma under hypnosis.

Thanks Joseph C!