Now most people know there is a distinctive difference in the way police work is portrayed in movies and on television and the way it is in real life. This is something that anybody wanting to run a police themed game will also have to decide on. Do you go with real life or the movies? Personally my recommendation would to always put quite of a bit of the movie/television spin into it. Here is a bit on why I say this.
A good chunk of actual real world police work is boring. Mind numbingly boring with very little excitement and lots of repetition. Directing traffic, standing in one spot telling people they can't come any closer to a crime scene for hours on end, paper work until your eyes bleed. This doesn't make for good entertaining game time. Now while I do urge folks to work some of the 'routine' assignments into the game from time to time I wouldn't make an entire game of it.
Bend the rules a bit on what an officer can and can't do. Let them do some of the investigative work instead of the detectives all the time. Instead of reporting everything and hoping their superiors take care of it let them follow up their own leads. Is this realistic? No. But is it fun or the players? Yes. Remember everybody having fun is the important part.
Give them the action filled chase scenes that almost never happen in the real world. The jumping over the car, gun drawn and bullets flying action. The damn near Parkour level of rooftop and alley way foot chases. When the excitement hits then make for sure that it's exciting. Because in the real world the 'exciting' part we see in the movies almost never happens.