Blue Steel(1990)

Rookie cop Megan Turner orders a burglar to drop his gun. He whirls to shoot. Too late. Turner fires, killing him instantly. When someone lifts the assailant's gun from the crime scene, the police hold Turner accountable for killing an unarmed man. That same someone carves Turner's name into the bullets and uses them in a series of murders. Turner teams up with detective Nick Mann to clear her name and catch the killer. But she is drawn into a deadly game of wits with a psychopath who's always one step ahead… and much closer than she thinks!