You will need to file part-year resident returns for both NY and NC for 2019 and report the income that you earned while living in that state on the appropriate part-year state return.
Here is a link with more information on filing part-year resident returns in TurboTax: How do I file a part-year state return? - Community
Plus here is more information with scenarios on filing a return in TurboTax when you moved to a different state last year: How do I file if I moved to a different state last ...
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