From what you are telling us, you accepted a deposit without any written agreement describing the nature of the deposit or suggesting that it was non-refundable, prior to accepting this person as a tenant. You are indicating that you subsequently demanded documents from the person as a condition of accepting him as a tenant, he declined to turn over those papers, and that as a result you rejected him as a tenant. As such, from what you have told us so far, you owe him a return of the deposit.

I understand not wanting to return his deposit because he was obnoxious, but you'll save yourself a lot of time and aggravation if you return it before he files a small claims lawsuit against you.