I would have firmly, but respectfully explained the situation to them again.
If they proceed to be arrogant, I would ask for their badge numbers and names, and their supervisors name so that I could report them for harrasing me, I'd write it in a formal letter, send it registered mail, and I'd call.
That said, I have respect for cops, and can understand where they were coming from. But IMO they took it a bit too far by being assholes about it.