Wait until you are sure the money has been deposited to your account. It is a bit odd for the state to pay twice and it may just be something in the banking system that makes it look like a double deposit.
If it IS deposited twice - DON'T SPEND IT! You don't say which state you are in, but you should write a check to the "Department of Revenue" and send it with a letter explaining you received two refunds. Don't do it immediately, but don't forget, either. Sometimes the state will catch an error and reverse it on their own. Give it a couple of weeks.
