State tax filing

Per the South Carolina Department of Revenue, you are a resident of South Carolina if you maintain your permanent home there, it is the center of you financial, social and family life and when you are away, you look to South Carolina as the place to which you intend to return:

So, New York would have no say in whether you are a resident of South Carolina. 

You can learn more about South Carolina residency status here:

https://dor.sc.gov/tax/individual-income/faq