Blue Steel

Blue Steel is a movie starring Jamie Lee Curtis, Ron Silver, and Clancy Brown. A rookie in the police force must engage in a cat-and-mouse game with a pistol-wielding psychopath who becomes obsessed with her.
Megan Turner, a rookie NYC cop, foils an armed robbery on her first day and then engages in a cat-and-mouse game with one of the witnesses who becomes obsessed with her.