What should my father do about false ual harment allegations?

My father worked as a Building Inspector for over 20 years, when he retired and is now part-time in a neighboring town. A few weeks ago he needed to inspect a propane heater or something. His inspection concluded that the heater ped. However, a coworker sent to light the heater said he would not have ped it. The whole rest of the day my father was worrying that he shouldn't have ped the heater, and that night he spoke to my mother about it. If my father was wrong and the heater was out of shape, this woman and her children who live there could have gotten carbon monoxide poisoning. My mother's advice was to go there and tell the woman not to use the heater yet, or to take another look at it. Long story short, the woman thought he was stalking her and called the cops. The cops believed my father and let him in to look at the heater. My dad concluded once again that the heater was fine. Since then, this woman has changed her story and filed a complaint that my father was ually haring her. She wants him arrested and wants to press charges. The chief said this "is a serious allegation." She is flat out lying. I've been distrought over this. What can he do to prove she is lying? Should he counter file for defamation of character or something like that?