A couple enjoys having sex while pretending to be other people.
They do this by stealing the identities of dead people--reading obituaries, getting copies of birth certificates, etc.
But when they steal the name of a criminal who's faked his own death, the police apprehend them.
They can't talk their way out of it, but then the detectives are assassinated, and the couple realize they have been framed--unless the find the actual culprit.
So they assume the identities of the murdered detectives and are off and running.
--E. R. O'Neill