I saw this film in the 80's or as late as 1992. Set in a city in the USA. The alien criminal is a being that takes control of humans (and in one case a dog) by passing from one to the next entering them through their mouths. The alien cop joins a local police officer and hunts him down. The criminal works his way to taking over the presidential candidate.
I found it so enjoyable I want to see it again, but can't remember the film title.