I believe that in nys if a person wants to become a LEO or a Police candidate they must go througha fairly extensive background check. I don't know if it is as exhaustive as the background checks for private citizens because we are less trustworthy in the eyes of the polticians who set up the rules but LEOs all have to go through a background check.
I would assume that a uniformed officer or any officer currently on duty, in contrast to being suspended from duty or somesuch, would already qualify as much as a ccw holder would qualify, and I believe that anyone wanting to purchase a Class II firearm (full auto) in nys would have to have a Class II License - I do not believe that full auto firearms are a 'over the counter' purchase for anyone in this state. jmtcw.