"Taxi!" is an earlier instance of James Cagney playing a character who calls somebody a "dirty rat." In "Taxi!" it's "dirty, yellow-bellied rat." In "Jimmy The Gent," it's "dirty, little rat."
Officer says "OK OK Buster" in a "you dirty rat" tone of voice. James Cagney said "Come out and take it, you dirty, yellow-bellied rat" in this film which in popular culture got simplified to "You dirty rat!"