Since he is your dependent, his resident state is your state, NC.
Technically your son should have had Kentucky tax withheld.
As a non-resident, he should file a non-resident Kentucky tax return and allocate the income he earned in that state.
Next, he would file a state return for North Carolina claiming all his income. North Carolina will give him credit for the tax he owes Kentucky.
The address on his W-2 doesn't matter.
I would ask the employer why they withheld NC instead of KY.
Kentucky does have reciprocal agreements with a few states, but North Carolina isn't one of them.
According to the state of Kentucky:
"Any net income of a nonresident shall be subject to Kentucky income tax if it is derived from services performed in Kentucky, from property located in Kentucky, or from income received from a pass-through entity doing business in Kentucky. Income from sources outside Kentucky shall not be subject to Kentucky income tax. Losses incurred outside Kentucky shall not be deductible in computing Kentucky adjusted gross income."
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