First of all, your tax withholding does not determine how your state income is allocated on your tax returns. Since you lived and worked in two states, you will file a part-year resident return for each one. As you are preparing each state return, there will be a page where you allocate the portion of your income that you earned in that state and/or while living in that state. It may or may not be the same as what is on your W-2.
If you did not earn any income in one state while living in another, the income allocated to each state will add up to the total income reported on your W-2 (Box 1). If you lived in one state while working in another, the amounts allocated to the two states will added up to more than the total income on your W-2. In the case of the later, the state you resided in while working in the other state will issue you a credit for tax paid to the other state so that you won't be double taxed.
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