If you are interested in RP for RP's sake then you might want to consider joining the Bretonia Police Authority.
I know that sounds a bit wierd as you would expect them to have to PvP when they are enforcing the law, killing the bad guys or forcing them to run outside of Breton jurisdiction, but you need to think again about that. I for one am absolutely useless at PvP, I couldn't hit a space station better than 20% of the time, even if I was trying Kamikaze attacks!
Having said that, since joining the BPA and patrolling in my Hussar LF, I have never had to use my guns, not once. I approach my RP with the belief that if a cop has to resort to his guns then he has failed at his duty of enforcing the peace. I even managed face down an Outcast Cruiser in the Cambridge system, alone and armed only with a pair of class 5 chain guns. I have to admit I was 'bricking it' during the incident, but he obeyed the law and exited the system without causing any trouble. A policeman's job is not to be a one man SWAT team, if he needs that sort of backup, he calls on our equivelant of SWAT, or the BAF.
If the thought of enforcing the law virtually unarmed and acting as a sort of unofficial 'Angel' (which is how I prefer to RP my policeman), to roleplay the friendly cop on the beat, then think about the BPA. And if you do fancy some PvP action, we do have SWAT specialist divisions as well.