Directed by Kathryn Bigelow, Blue Steel (1990) stars Jamie Lee Curtis as a rookie police officer who becomes the target of a violent criminal after a shooting incident. Set in New York City, the film follows an escalating cat-and-mouse dynamic between cop and killer. The story combines police procedure with psychological tension and urban crime elements.

Från IMDB:
A rookie in the police force must engage in a cat-and-mouse game with a pistol-wielding psychopath who becomes obsessed with her.