Yes, that is correct. The individual would file a nonresident New York return. The individual would also file a part-year resident return for North Carolina and a part-year resident return for Colorado. Both states will give them a credit of taxes paid to New York for the time period in which they were a resident.
There are no credits that you need to list in North Carolina and/or Colorado that would offset each other.
@jg5statetax
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