Copycat
(1995)

Finally, after killing a bunch of people, teasing Helen (Sigourney Weaver) with threatening messages, and breaking into her apartment a couple of times, the killer – Peter Foley (William McNamara) – makes his move on Helen one night. Disguised as a policeman, he openly confronts her in her apartment, drugs her, and then takes her to the exact same place where Darryl Lee Cullum (Harry Connick, Jr.) tried to murder her a year before, and seeks to kill her the same way in which Darryl tried to.

Detective Monahan (Holly Hunter) figures out her location after watching a tape Peter left back at Helen’s apartment, and though her initial attempt to help Helen results in her getting shot and seemingly killed, it buys Helen the time to get free of her restraints, temporarily subdue Foley, and escape to the roof. Foley gets up there, but before he can kill her, a recovered Monahan shoots and kills him.

It last shows Darryl writing and mailing a letter to another serial killer, instructing him to kill Helen since Foley failed him. 

Thanks Tornado Dragon!