What is the name of this classical time travel crime movie?

[BenkieDNA]

I cant find the name of a 90s time travel movie that begins with that a man is going back in time into a bank where he is chocked about being back in the 50s and he talks to someone in the bank handling money and it is about a stolen identity, a killer has taken the man that travels back in time identity so he looks like a copy of him, and he is a serial killer, and a cop gets involved and tries to catch the killer, and in the end of the movie the guy that travles in time meets a woman in another dimension that tells him some secret about the world.

I am not talking about Gattaca from 1997.