I agree, record the critter, log the time and duration. Check with local ordinances. If nothing else set up a automated recording/logging system. You do not want to injure the dog nor get into who is the bigger neighborhood nuisance competition with the neighbor, both of which would put you in legal hot water. If the police (non-emergency call) can not do anything about it, You might seek a lawyer and see if you can seek some sort of compensation for the lost peace of mind.