This is a semi-serious RP server, and calling it semi-serious is a stretch. For the most part, people come here for the combat. It's probably one of the best servers on ArmA 3 for pvp, and is FOR SURE the best Altis Life server for pvp.
Seems you're new here, so I'll go into more detail. There's pretty much two types of classes on this server: Civilians and cops, with civilians having a few sub-classes: Rebels, Bounty Hunters, and the good ol' regular civ.
Most civs are either bounty hunters or rebels, you're the small few who play as just another dude. Well, these servers are far more centered around the combat aspect of rebels, bounty hunters and police than they are around you, the regular civilian. Not to say theres not enough content for you to enjoy, theres more than enough.
My point is, the next time you get into this situation, and you will, remember that whatever rules you're used to from serious rp servers are almost always non-existent here. In fact, the only form of NLR on this server is no revenge killing (Killing someone that just killed you without engaging in roleplay first). Your obligation for roleplay stops and ends with you saying "Put your hands up or I'll kill you". If they comply, you can't kill them. If they don't comply within 3 seconds, blow their ass away.
You don't need to ask some body for their name before you "know it". You don't need to pretend you're a different person when you respawn. You don't need to worry about "breaking character" when talking to the police or another civ. However, police officers must remain in character as best as they can. There are times where they might have to break character (e.g: You're bugged, I'm gonna have to down you), but police are the only ones who MUST rp at all times.
I'm curious to know what you told the officers. If you told them you and your friends were held up, they should have cut you a break at least. But keep in mind, you don't need to tell them what actually happened. Go a little crazy with your roleplay. Have fun with it. Instead of being a boring, monotonous criminal, tell them you're a astronaut and your spaceship crash landed on Altis and crushed two people to death and you're terribly terribly sorry. Or do the old "two people were raping my dog" story, that's a big hit in the APD.
If semi-serious roleplay isn't your forte, well, you won't have fun here, but at least try it out for another week or so. I think you'll find that, at it's best, Asylum has the perfect balance of roleplay and combat. Personally, the time I've spent on this server has been THE BEST video game experience I've had since I started playing games on my gameboy color.
EDIT: One more thing, I personally feel the semi-serious roleplay breeds much more interesting roleplay. Some of the funniest moments I've had in a video game came from some of the RP i've witnessed on Asylum.