If you have any Capital Gains on the sale, your resident state will give you credit for income tax paid to North Carolina on the gain.
Click this link info on How to File a Non-Resident State Return.
When you report the sale of the North Carolina home, be sure to use the FMV as of the date of death, and add the cost of any improvements to the 'Cost Basis' when reporting the sale. Travel expenses are not deductible since it was not a business property.
This link has detail on How to Enter Sale of Second Home, Inherited Home or Land.
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