My mom lives in a retirement apartment community. It's arranged so that each apartment building is 4 one story garden style apartments. This gives everyone some green space to garden or whatever. Due to health issues mom likes to take walks. Her neighbor approached her and told her that she was going to start calling the police when she sees my mom outside. This woman is unstable and moved into the community from a mental health facility, so my mom decided to ignore her and try to avoid the situation.
Yesterday, the police came to my mom's and told her that the neighbor has been calling them continuously for the last week. She is making all sorts of accusations such as my mom beats on her windows and threatens to kill her, my mom is beating on the walls, my mom is having an affair with this woman's boyfriend. Long story short, she finally hit upon something that was illegal, so the police had to come. (Death threats) My mom is in poor health. She literally sleeps like 18-20 hours a day. We have no idea why this woman has started this campaign. Mom asked the police what she was supposed to do to get the woman to stop calling when she isn't doing anything to cause her to call in the first place. (How do you stop doing something you aren't doing?) The police told her that if the phone calls to them didn't stop, then they would have to do something, implying that my mom would be accountable for the false accusations.
I know this whole thing is absurd. I just don't know what to do about it. How can we get the police to hold this woman accountable for false accusations? How do you prove you aren't doing something?
We live in the state of Missouri.
Any advice would be appreciated.

