Second Home Sale

Yes. Income from a North Carolina source is subject to tax by North Carolina. Since you are a Kansas resident, all your income is subject to tax by Kansas, no matter where the income is from. But you will get a credit on your Kansas tax return for part or all of the tax that you pay to North Carolina. The credit cancels out the double taxation. Prepare your North Carolina nonresident tax return first, then your Kansas resident tax return, to make sure that the credit is calculated correctly. If you have already done them in the opposite order, go through the Kansas interview again to calculate the credit.

You should not have to pay tax on the same income in both States.

Make sure you indicate in the TurboTax My Info section that you earned income in another state.

Complete your non resident state return first.

When you do your Kansas return you will be prompted to allocate your income.  You income from non Kansas sources will not be taxed by Kansas.