Just to re-iterate, the LPI aren't terribly good people. Read some of the news reports about their conduct in raiding campgrounds and the like to round up some of the "wont be missed" people to take a hand at sowing wallets on Huntsville and the like.
The Xenos need another enemy like they need a hole in the head, but the LPI was well known for their long run war against their ilk in Colorado 'afor the Xenos got their act together and started to do things proper, the LPI almost ran them out of the system as a matter of fact.
If you run in, yell "freeze" and everyone does, run a quick check and demand they come in with you to Fort Bush for questioning back at the precinct, I've a vague suspicion they'll decline!
Though, on that same token, were you on a different case you could tell 'em to shaddap and answer a few questions, ask about party X passing through the area etc etc as you're not worrying about them that day. Though what right minded Xeno would co-operate with an LPI Detective as shoot at him is beyond me!
Just my own mulling, not like I've any foundation for suggesting conduct and such things to you!
Oh, and as for Bounty Hunter ships being Crown Vics with targets painted on them, no. Liberators are the Crown Vics of this game, and if Detectives want to fly marked cars, that's fine. The Bounty Hunter line may be labeled as 'lawful', but they're no police ships.
With your input, I think we can put Xenos to 'shoot on sight', OK? Since they're terrorists and all.