Enter that income on your federal return. The information flows from your federal return to the state return. NC does not tax Social Security. If the other income you received is taxable in NC the software will follow the tax laws for the state.
https://ttlc.intuit.com/questions/1901227-how-do-i-file-a-part-year-state-return
https://ttlc.intuit.com/questions/1901560-how-do-i-file-if-i-moved-to-a-different-state-last-year
https://ttlc.intuit.com/questions/2895983-how-do-i-allocate-split-income-for-a-part-year-state-retur...
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