Both states have loan programs to help pay for your down payment, if you qualify, but not an actual credit.
However, I did notice that North Carolina has the NC Home Advantage Tax Credit program. This is not a credit on a NC return, but is a federal tax credit related to the amount of interest you pay. As the state notes: "The NC Home Advantage Tax Credit enables eligible first-time buyers (those who haven't owned a home as their principal residence in the past three years) and military veterans to save up to $2,000 a year on their federal taxes with a Mortgage Credit Certificate (MCC)." See this NC webpage.
Note that this is a federal tax credit, not state. If you qualify for the state program to get an MCC, then you would complete form 8396 on your federal return to calculate the credit. Please see About Form 8396.
Since your home is in NC, this seems like the appropriate state to pursue this in.
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