A Neighbour Has Falsely Accused Me Of Being Threatening What Can I Do?

Set up some surveillance cameras on your property, but don't point a hand held camera at the neighbors as that can be considered harassment. Make a statement saying you did no such thing and scribble in all open spaces so nothing can be forged on you statement and say nothing to the police if they had anything on you they would have arrested you. You could file a report at the police department for harassment on the neighbors and the police department. I would get a lawyer asap.

You probably won't like my answer, but you need to consult a lawyer.

Your demeanor and behavior during the interview with the police will clue them in as to the truth.  Your neighbor probably comes across as a nutcase, but the police have to follow up on the call.  So just be honest with them and let them do their job, and leave it at that.  The neighbor may be guilty of filing a false police report.  If it persists, videotape some of your neighbor's strange behavior and that will help you.