If your home of record is West Virginia but you did not spend more than 30 days in the state during the year, you are not treated as a West Virginia resident for tax purposes and you owe no state income tax on your military income.
There is nothing to apply for. Do not file as a West Virginia resident for a year in which you spent 30 days or less in the state. If West Virginia tax was withheld from your military pay by mistake, file a return to claim the refund.
Your Leave and Earnings Statements and orders showing where you were stationed, and a record of the days you spent in West Virginia.