I've been putting up with that crap from a wacko SIL who says I'm stalking her and threatening her. She says she's going to go to the police, hasn't yet, but I've already been expected by one family member to somehow *prove* I wasn't doing it. I shudder to think what problems she could be causing me if she wasn't such a drunken moron. I actually considered anonymously ordering a couple of cases of vodka to be delivered to her house in the hope that she'd drink herself into a coma.
Point is, she goes to the cops, she doesn't have to provide any real evidence, just make the claim in order to cause me problems.
You should probably be documenting this very carefully and thoroughly. Threatening you with false arrest is probably a crime.
I would, at the very least, get written statements from any witnesses to her false and malicious behavior. At some point such evidence might be sufficient for a restraining order. I certainly wouldn't just ignore such threats.
There appears to be a presumption, perhaps slightly justified, that the first person in a conflict to call in the police is the one to be believed. You may want to be that person.
I'm not a lawyer, but if this was happening to me I would be consulting one with the reasonable expectation that the transgressor would eventually have to cover my legal costs.