the question is did the tenant give you any forwarding address?
the question is did the tenant give you any forwarding address officially?
if they turn in the key and officially give you a forwarding address, you bound by law you must send a detail statement, within whatever day your state law require, or you must refund the full deposit plus attorney fee.
if they just thru you a key, and didn't give you anything in writing, then don't worry about it, go fight for it.
new landlord need to learn this lesson.