If the employer issued a corrected W-2 showing less state tax withheld (or no state tax withheld), the employer has to refund the incorrectly withheld amounts to you. The fact that the employer issued the corrected W-2 shows that the states did not get the incorrectly withheld amounts, so you cannot get the refunds from the states. Your W-2, with the corrections, shows the amounts that the employer actually paid to the states.