Classical time travel crime movie from 90s?

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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.



I'll throw out the TV series, Life on Mars, which is a cop show involving 'time travel'. There was both a British(2006-2007) and American(2008-2009) version of the show.

I've never seen either series, but those popped into my head.



Not Timecop (1994)?

__________________
"Film is a disease. When it infects your bloodstream it takes over as the number one hormone. It bosses the enzymes, directs the pineal gland, plays Iago to your psyche. As with heroin, the antidote to Film is more Film." - Frank Capra



I found it! The Thirteenth Floor.