Here's what I believe:
Laddy is either an insane cop, a paranoid cop, or a real cop. I do not think his roleclaim was a mafia ploy to get Psychotic out of the game. It's just too early for that. And I'm not sure why Psychotic thinks it was. Since he's mister 'lets talk things out for 50 hours', his immediate vote for Laddy seems very suspicious.
Psycho: I don't think you came up with it on the fly. I think you planned it from the beginning.