Arkansas does not tax the military pay you earn while serving in an active or reserve component of the U.S. Armed Forces. The pay is fully exempt from Arkansas income tax.
There is nothing to apply for. Leave your military pay out of the income you report on your Arkansas return. If Arkansas tax was withheld from it by mistake, file a return to claim the refund.
Your Form W-2 and Leave and Earnings Statements showing the military pay, kept with your tax records.