I highly suggest you contact the bank to let them know of the situation ... if the state does deposit the refund to the wrong account they will not be responsible and will not reissue the refund or help in getting the refund back.

Not all banks check the name on the account. Your bank might not reject the deposit. If they accept the deposit to the specified account number, you may have significant difficulty getting your refund. The state and the bank followed your instructions. They are not at fault.

Did you intentionally send your state refund to the bank account of someone you know, or did you just enter a random incorrect account number?