Mich. Comp. Laws § 141.659

Sec. 59. Correction of an over or an under-withholding as a result of an employer's error shall be made as follows: (a) If the error is discovered in the same quarter in which it is made, the employer shall make the necessary adjustment on a subsequent pay and include only the corrected amount on the quarterly return. (b) If the error is discovered in a subsequent quarter of the same calendar year, the employer shall make the necessary adjustment on a subsequent pay and report it as an adjustment on the quarterly return. (c) If the error is discovered in the following calendar year, or if the employer-employee relationship has terminated, the procedure shall be as follows: (i) The employee or former employee shall apply to the city for a refund in case of an over-withholding. Upon proper verification the city shall refund to him the amount of the over-withholding. (ii) If a deficiency is discovered, the employer shall notify the city and the employee or former employee, who shall pay the city the additional tax due in his annual return.