You can deduct your military retired pay from your North Carolina adjusted gross income if you served 20 or more years or were medically retired. Thrift Savings Plan money is treated differently: no state tax is withheld from it, but all TSP distributions are subject to state tax and early withdrawals can be taxed more heavily.
There is nothing to apply for. Claim the deduction on your North Carolina return when you report your federal adjusted gross income.
Your Form 1099-R showing the retired pay, and your DD214 or retirement orders showing your years of service or your medical retirement.