Minnesota does not tax the military pay you earn as a resident serving in an active or reserve component of the U.S. Armed Forces.
There is nothing to apply for. Take the military pay subtraction on your Minnesota return and leave the pay out of your Minnesota taxable income. If Minnesota tax was withheld by mistake, file a return to claim the refund.
Your Leave and Earnings Statements or Form W-2 showing the military pay, kept with your tax records.