I found another answer that says to enter both states on the same W2 in TurboTax, which I did. I entered the non-resident state first with income and taxes paid as shown on that W2 and then entered the second state on the same W2 in TurboTax (there are multiple rows for states in box 15) with income, but no taxes paid- as shown on the W2 I received. TurboTax then calculated a refund from the non-resident state and an amount due to the resident state. From what I understand, the states will handle these amounts behind the scenes.
