It depends, but probably not. If this was your personal home, and you lived in the home for at least 2 of the last 5 years, you can exclude up to $250,000 of the gain on the sale from your taxable income if you are single or a Head of Household, and up to $500,000 if you are filing Married Filing Joint. You would only have to pay Federal and State tax if you did not have the home long enough or you gained more than $250/$500 K on the sale for a personal home.
If they are both rental homes (your question doesn't suggest this, but just in case), you would also not have to pay any tax now if you were to elect a Like-Kind Exchange Treatment. Under this arrangement, the new home essentially would acquire the basis on the first home through the election, and you would defer, or postpone, including the profit of the sale in income until you sold the NC property and did not have another qualifying property to purchase for a continued Like-Kind treatment.
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