Your military pay is fully exempt from Vermont income tax if you are a Vermont resident on full-time active duty in the U.S. Armed Forces and you are serving outside Vermont.
There is nothing to apply for. Leave the exempt military pay out of the income you report on your Vermont return. If Vermont tax was withheld by mistake, file a return to claim the refund.
Your Leave and Earnings Statements and orders showing that you were on full-time active duty and stationed outside Vermont.