Legal Question in Insurance Law in New York

Re: How can I prove someone damaged my car?

Your real problem (apart from the fact that your neighbor is a lying bottom feeder) is that the expert lab report and testimony you would need to establish that it's your paint on his mirror is almost certainly more than the cost of repairing the dent. Absent some access to affordable scientific experts, or some serious reputational damage that you can inflict on the person-who-is-not-nice, there's not a whole lot you can do. However, you could try to become a highly skilled Vajrayana Buddhist and ascertain what kind of slug your neighbor will be reincarnated as. That might be some satisfaction.