DH and I have sort of been there in the past....not a tenant but same sort of thing...took legal advice (we had legal insurance at the time) and was told to ignore which we did. Legal beagle said that police would not be interested in allegations made to a third party and would only be slightly, if at all, interested in unsubstantiated allegations unless they were the kind that they HAD to take notice of, eg child abuse.
From what I know of your situation, my personal, not legal advice would be to try and think like a business and not a person and ignore the dross and focus on the admin. Different of course if this person has made threats against you and you can prove it.