If you worked for the same employer, and they reported all of your wages under the same EIN (Employer ID Number), then you would report all of your wages once in TurboTax, whether or not they issued more than one Form W-2.
When you get to the State Taxes section (Boxes 15-17), enter the information for both states (income and withholding) on just one W-2 even if you received two separate forms from your employer.
You can add more lines/boxes if necessary by clicking on the link "+Add another state".
See this help article for more information.
You would file part-year resident returns for each state where you worked. Prepare the nonresident (state you moved from) return first. See also this TurboTax article on multiple-state situations.
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