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This must feel like a bizarre situation; you did not have to go out looking for trouble--it just came to you.
It is not per se illegal to list someone else's address as your own, but it can be in certain contexts. If the address is being used fraudulently to obtain a public benefit, to register to vote, to avoid law enforcement, etc., then it usually constitutes a criminal offense. This can be surprisingly difficult to prove because it is in the context of "intent", but that is where law enforcement steps in.
On the other side of the coin, if this person's error (whether deliberate or accidental) somehow caused you damages, you could have a civil cause of action against them. However, that is pretty unlikely and there is probably no money of his to get.
Hypothetically, if this was done deliberately with the intent to harass, annoy, embarass, etc., you would have a cause of action for a civil restraining order; thereafter, if it continued, there would be a criminal cause of action. The problem with that, though, is that the guy is probably not going to be easy to track down... afterall, you obviously don't have his address.
If it gives you any comfort, I worked as a deputy district attorney before my present work in the civil arena, and I can tell you that it is extremely unlikely that this person has any intent whatsoever of having any contact with you. Based on your description of events, it sounds like the guy was released on probation and he gave a bogus address so his probation department couldn't keep track of him. This is not terribly uncommon. Under these circumstances, the last place (or second to last place) that he would want to show up would be the residence where he told them that he resided. Besides, why would he show up? To get arrested for violating probation? To collect his mail that he obviously didn't want to begin with? I understand that this would feel unsettling, but let me provide logic within the confines of my experience to assure you that the likelihood of ever encountering this person is slightly more than nil. I am not going to tell you to not watch out for anything suspicious, but (based on what you have said) it would probably be a mistake to in anyway alter your daily affairs. Best of luck.
Was there anything else that I could assist with on this question?