Yeah, revenge is sweet and all that, and all the testosterone pumped adolescents will recommend punching the son of a bitch in the face, or worse, but if I were you I’d seriously consider moving.
If you can get evidence he did it, the police get involved, he gets jail maybe, or a fine, sooner or later he’s back next door. Hating you, and looking for worse ways to “get even.”
If you cannot find evidence he did it, then, either he didn’t do it, or he did. If he did and you can’t prove it, he feels like he got away with something, and the next thing you know, he’s up to something worse (why? because he thinks he can get away with it, he’s a nut, remember?)
If you can’t prove it because he didn’t do it, then he winds up with a somewhat legitimate grievance against you that in a normal person wouldn’t be a problem, but with a nut will simply convince him to actually do something to justify his “reputation.”
You are in a lose, lose, lose situation. People like that bring out the worst in everyone they come in contact with. Break contact. Life’s too short.