Yes, you will file part-year resident returns for both IL and NC. Your W-2 will show the current address your company has on file for where the W-2 was sent to get to you. Also, your income is not broken down by months, but rather into yearly totals. However, your Illinois income should be listed in boxes 15-17. You should see one line that says IL and another line that says NC.
Nevertheless, if your W-2 only has one state mentioned, and the amount in box 16 matches the amount in box 1, you are still required to file in both states. In this case you would allocate your income on your part-year returns. You would determine the percentage of the income you earned while living in Illinois (roughly 66%) and multiply that by your total income. If no IL tax was taken out (only NC tax), you leave the Illinois tax withheld at zero, which means you will have an amount of tax due. However, when you file the NC return, you will have paid a full-year's worth of tax on only 33% of the income, so the refund there should make up for most of the difference.
Those are "just-in-case" instructions. It will be highly unlikely that your IL income is not reported, especially since you were living in IL at the beginning of the year, before deciding to move to NC. Your company would have been withholding IL tax at that time.
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