Advice for end of lease/tenant double paying last month's rent

[Jarrod B.]

Hey All, 

I was wondering if you could help me out here with some advice.  I have a 12 month lease that ends May 31st.  Of course they paid first, last and security deposit, so really and truly if he were moving out he would have already paid for May's rent and of course he would move out May 31st.  

I sent them a rent increase notification April 29th letting him know if he intends on renewing for a another 12 months, the rent would increase beginning June1st.  He sent a brief response indicating that he was going to stay, but then sent me a long email today trying to negotiate the new rent and blah blah blah.  So he didn't renew.  Normally, I would tell him to pound sand and get him out by May 31st (he hasn't been the best tenant in the world), but the problem that I'm having is I have him set up on direct deposit with my checking account and he deposited the rent for May in addition to having paid the last month's rent when he initially signed the lease.  If he just wrote me a check, I wouldn't have accepted it until he renewed, but since he double paid for May, can I still legally tell him to get out May 31st and then reimburse him for the last month's rent in addition to the security deposit?  Or am I somehow entitled to allow him to stay for an additional 30 days because he paid in May?

Your help and wisdom would be greatly appreciated.

Thank you,

jb