You're bound to get some cops that are dicks, he might have stayed alright if you had moved on, but its all about rights. PUBLIC park. By the way you have worded it, he didn't even try to negotiate and it sounds like he couldn't be bothered to give you the time of day so he just nicked you. You sound a bit like me, a decent fella who's considerate of other people, and if that situation happened to me i would have stuck up for myself and questioned it too, because all people shouldn't get tarred with the same brush. Also there's no need to push you to the floor if you weren't behaving violently, you see it on those police camera action type things where even when people are starting fights and pished out of their faces they get asked to put their hands behind their backs etc not just wrestled to the floor. If a cop arrests you, you have the right to ask for his name and badge number and i think a written reason for arrest as well. Might be worth doing next time so you can take it further with half a chance.