I don't think that a cop is going to investigate the trusted people.

Why I think this.

A. If the person is trusted why bother? Cops go right after "suspicious" ones

B. In order for a cop to say "Don't trust him! He's mafia!" he has to reveal himself, if he does that, then sure, our leader dies, but at the very least we know who's the cop, and can try and kill him if the doc is dead.

C. Not everyone will go along with the fact that he's a cop, if that would true, you would've been dead instantly last round Lev'.