Its hard to think of things like this when the man is breathing down your neck like that, but if the motor was off it'd be cool to the touch, correct? " Hey, the motor was off, feel how cool it is..."
I don't really get what you say, were you grabbing the side of a trolley and having it pull you? or were you just riding to the side of where the trolley runs on the street?
So many laws to try to sort, cops can just make stuff up and charge you for whatever pops into their heads at the moment. Do your duty and go to court to fight it!