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Deductions & credits
No way to know for sure because it depends on your actual taxable income each year. And whether you are married or not has a big effect too (working spouse or not too).
.....NY has a progressive tax rate of ~ 4% up to ~8.8%. NC has a flat rate of 5.25%.
Taxable income is your gross income, minus your allowed deductions in each state. The standard deduction is different for each state too...itemized deductions allowed may be different too, so there is no way any of us can give you a definite answer.
Look at the tax tables for NY and NC here....(but remember, the tax rates are applied to your income after deductions are applied)
https://www.tax-brackets.org/newyorktaxtable
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Of course, if you have the time over a couple weekends, you could buy the 2019 desktop software (Deluxe or higher) and model each of your potential income situations using the 2019 software (should be close enough to 2020 or 2021) . You'd get one free State software set, but would have to buy the other state software set to do all of the state calculations. You could then use your 2019 tax situation, and create tax files for fully in NC-resident, and a separate one for NC-resident plus NY-nonresident. (Don't attempt to use the Online software, especially if you used "Online" for your 2019 taxes)