Yes, you need to file both NC and SC tax returns.
If all of his work had been performed in SC, then you would only file a SC return. Since he actually worked in NC certain days, then the income for those days is NC source non-resident income and should be reported on a NC tax return.
Since the income is reported on Form 1099-NEC, you will need to include a Schedule C to report it. After the Schedule C is finished in the Federal return, you will have a final business income amount. This final Schedule C income will need to be prorated and reported on the state returns according to the number of days worked in each state.
Be sure to claim the tax credit for taxes paid to another state on your SC return based on the NC tax return. Complete the NC tax return first and the numbers for the tax credit should automatically populate on your SC return.
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