For state of residency, you will select NC and for previous state select WA. Since you will be in NC for more than 12 months, NC will consider you a resident of the state. For 2024, you would only be a part year resident.
In your situation, it is not going to make much of a difference on your return. Regardless of your residency status, since you are earning the money in NC, you would have to pay taxes on it. Since your "home state" does not have any income tax, you will not have to include your NC income on another return.
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