1. Any income you earn from work you perform in New York is taxable by New York regardless of whether or not you are a New York resident.
2. If your move to New York is temporary, and you stay in New York fewer than 184 days of the tax year, then for tax purposes you will file as a non-resident of NY and a resident of NC. In that situation you'd be able to claim a credit on your NC return for the taxes paid to NY, so you wouldn't be double-taxed.
3. If your move to New York is intended to be permanent, then you become a resident of New York on the first day you begin living there. In that situation you'd file a part-year resident return in each of the two states.
https://www.tax.ny.gov/pit/file/nonresident-faqs.htm
If you're going to be working in NY, you should have NY taxes withheld from your pay, even if you do not become or plan to become a New York resident.
Your tax obligations are not determined by the mailing address on your W-2. Instead, they are determined by state law.
Post back if this doesn't answer your questions.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
