Minnesota does not tax military retired pay, so your military pension is fully subtracted from your Minnesota taxable income. Thrift Savings Plan money is different: no state or local tax is withheld from it, it is reported each year on IRS Form 1099-R, and all distributions are subject to state tax, with early distributions possibly taxed more heavily.
There is nothing to apply for. Take the military pension subtraction on your Minnesota return. Do not also claim the credit for past military service for the same year, because you cannot have both.
Your Form 1099-R showing the retired pay, kept with your tax records.
