The New York City Police Department, or NYPD, is the main police department in the show. It's where Robert and his partner Judy work.
Also, actor Ray Romano's brother in real life (Richard Romano) is a cop for the NYPD. He made a few appearances in the show, some of which were in uniform.
There is an embryonic Wikia for the NYPD and it may be found here. Interested people with inside knowledge might want to help it along! Its page on NYPD rank distinctions is interesting, in the light of Robert's promotions in the force.