British police officers are pretty good in my opinion, I've spoken to a few in order to get directions a while back, they were some of the most friendly police officers I've encountered.
In the USA though I have no idea, and frankly I wouldn't want to test it out. I've seen numerous clips on the internet of people being shot dead for taking their wallet out of their pockets, and I'm not even sure I blame them considering the widespread prevalence of concealed firearms there.
Here is one clip I'm talking about, where there was no suspicion of any armed individual or crime, and police were just responding to a minor traffic accident. (Warning there is a bit of graphic content.)
They were not pursuing any armed suspect, nor was there any hint of a crime being committed. It was a minor traffic accident where a guy accidentally clipped the back of a truck.
@TaiShang