Where prompted in TurboTax, enter the dates you lived in each state. Since you were in Colorado at the end of the year, prepare that return last and prepare a part-year resident return for New York first after the Federal return. You may be able to claim a credit on the Colorado return for taxes paid to New York.
For more information on this topic, see Multiple States—Figuring What's Owed When You Live and Work in More Than One State.
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