Before I Wake (1955)

"If I die before I wake this note will reveal The Killer..."

A woman travels to England to attend her parents' funeral. She is told by officials that they died of natural causes together, but she doesn't buy it. She comes to suspect that the nurse who took care of her parents was involved in their deaths, but since the nurse is well thought of in the town, no one believes her. What she doesn't know is that her parents' killer has selected her as the next victim