By sheer coincidence I was chewing over the same topic [of armed police helicopters] with a European correspondent and the matter of armed helicopters in the USA came up.
Firstly it was clear that the JAA takes a dim view on arming civil aircraft. One national arm was 'obliged' to move from civil registration to government aircraft in 2000 over that issue.
Nearly all US police aircraft are armed.... in general this relates to personal sidearms [in case they come down in bandit territory?] but a few [civil registered] units carry machine guns and make a big thing of spraying a bit of their local Californian desert with practice rounds to keep their hand in.
Quite which brand of 'customer' would require this treatment is unclear.
If the JAA doesnt like it it might be assumed that the FAA ought to follow ... not so it seems in California.