The crooked cop is a gangster. The only difference between him and the normal gangsters is that every day he can ask the narrator who did the detective investigate and get an answer.
The moment the detective is out of the game, the crooked cop becomes a normal gangster.
Same with the recruiter. The difference between him and the other Gs is that once in the game he can recruit a civilian. After he does that he becomes a normal gangster.
If there are 4 gangsters in this game, 2 are normal Gs, 1 is a recruiter and 1 is the crooked cop.