Ya, but IMO, being a good neighbor is walking over and knocking on the door and saying Hi, My name is ____ and I am your neighbor, how are you today. Good to meet you. blah blah. Hey listen, that tree limb, can we work that out sir ? I can pay someone or do it myself or you can what are you comfortable with yadda yadda.

Resorting to lawyers deserves a shit stain unless the above does not work first.