I have a tenant in a house in Maryland. The tenant did not sign a lease. He has failed to pay to several months rent and then just moved out. He did provide a security deposit. Can I use that security deposit to offset past rent and damages to the house.

Definitely write up an itemized detailed damage document.
I am not sure that legally you can with hold it for rent owed but it would make sense that he wouldn't fight it unless he WANTS dragged through court.