My question involves a security deposit in the State of: New York City

Hello,
I recently rented a room to someone. I am the only lease holder for the apt. The agreement, stated up front in my advertisement, and in my interview, was for no less than 6 months. The individual gave me the first month and 1 month security deposit. 1.5 months later he tells me he is moving out in 1.5 months. He tries to tell me he's going to use the security deposit for that and pay me half a months rent. I told him no way about using the security deposit in advance. I told him that the contract was for 6 months. He said that was never in writing. It was in writing on my end but he never signed. Yet he did agree to it verbally and him being in the room obviously shows that he did agree. Otherwise I would have picked someone else.

He becomes very aggressive & starts complaining about things that he didn't like. However, he clearly stated he is moving for pure convenience, not because of any of those things. He was just employing the defensive offensive. I told him that nobody stays in my apt. without a security deposit, so he paid me the month of April.

This guy was originally scheduled to move in on a Fri. and on Thurs. night he emailed me and cancelled the whole arrangement, stating that he was moving in somewhere cheaper. Sunday he shows up at my door (with his mother) stating that he wasn't able to move in after all, that he was going to start a new job on Monday and could he please take the room. I had interviewed other people over that weekend and I had a person who wanted the room and who was perfectly suitable. But I felt bad for the individual & seeing that his mother was involved, I thought it would be OK. Obviously, I did not trust him too much after what he pulled. After I said ok, the mother asked me if I would lower the rent. I told her that there was a portion of the charge that is for cleaning. My experience is that people don't clean & so I just charge them and then it doesn't bother me. So he agreed to clean for a discount of $50. He didn't clean but I wasn't going to say anything since I had no intention of keeping him after 6 months anyway and I'd go back to reinstating the charge.

Anyway, I held some of the guy's stuff in my kitchen and the person who was occupying the room (another one who broke the 6 month agreement) left in a hurry. She wanted to anyway but I told her that she needed to give me 1 month notice, which was why she was still around. I gave her back all of her deposit.

So, what a surprise that this guy is a flake. The biggest issue is that I am going away in the summer and I do not want a new person in my apartment, with access to all of my things, while I'm away. I need to know them a little first.

The question is: am I obligated to return his 1 month security deposit and if so all of it or what? His intentions were not honorable. He admitted that he made a deal but said he never signed it. My 6 month minimum was prominently displayed in my ad and it was discussed verbally. But he could later lie and say I gave him a waiver though. So what are my options here?