No North Carolina tax return is required for your son unless he earns money outside of his military income from North Carolina sources. Since his home state of record is Texas and there is no state tax income tax required in Texas there would be nothing he can deduct. This is not a deduction for federal tax purposes. If there is personal property tax, which is charged based on the value of the vehicle, this is allowed as an itemized deduction on the federal return.
Only state returns, and not all states, allow a deduction for the vehicle registration fees.
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