You need to decide if you are a resident of NC or NY or if you changed the residency in the middle of the year.
You should file first the state tax return where you are a non-resident. - As a non resident you will be taxed only on income from that state.
Then - you will file the state tax return where you are a resident. - As a resident you will be taxed on all income regardless of its source. However as the some of you income is taxed twice - for non resident state and for home state - you will claim a credit on your home state tax return for taxes paid to a non resident state.
On federal tax return - you will combine all income from both states.
Let me know if you need any help.
Tax Preparer
Personal Investment, Tax Preparation