My neighbor lied to the police and said I was selling narcotics on my property. What should I do legally?

Legally, there is not much you can do other than be courteous and compliant when the law shows up at your door. If you try to sue him, your taking a chance of losing in a court of law and also being out the expense. All he would have to say is that he felt he was doing he civic duty and really thought there was drug activity going on, especially if you have a lot of people going in and out of your place.