You definitely want NC taxes withheld, if your employer will do that for you. Here's why: on the day you became a resident of NC, you became liable for NC state income tax on all your income from that date forward, regardless of where you earned it. As an NC resident now, you will definitely have to file an NC tax return for 2016.
If you've lived in NC all this year, you'll file a NC resident state income tax return for 2016. If you moved to NC after January 1, you'll be filing a part-year resident return in both NY and NC, allocating your income between the two states based on dates of residence in each.
Once you became an NC resident, NY could no longer tax you unless you earned income after the move from physically working in New York - for example if you went back to the home office for a couple of weeks and did some work there. NY does have a "convenience" law referred to by SweetieJean, but I do not believe it would apply in your case (just my unofficial opinion). I believe the law is aimed at people who (for example) work in NY, live in NJ, take a few weeks off and do some work from home, and then claim that the income earned while they were home in NJ is not subject to NY tax. You can read the text of NY's law here and decide for yourself: https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
Or you could call the NY Dept of Taxation and ask them about it: https://www.tax.ny.gov/help/contact/
Finally, if your employer cannot or will not withhold NC taxes, you should definitely consider making some estimated tax payments to NC.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
