It depends. Adjustments to income are usually items like moving expenses, student loan interest deduction, IRA deduction, and other so-called above-the-line deductions. (As compared to itemized deductions). The question you ask usually comes up when you are doing a part-year return for a particular state. These deductions usually must be claimed proportionately, that is, based on the amount of income you earned in each.
For example, let's say you live in State A, where you earned 30,000 in the year, and then you moved to State B, where you earned 20,000. Because of your move, you were able to claim a 2,500 deduction on your Federal Return. However, you can't claim 2,500 deductions on both states; you must allocate, apportion, or split them. In this case, your split is 60-40, and you claim 1,500 of the adjustment to State A and 1,000 to State B.
That is a general guide; if you need more specific information please be sure to comment so we can provide additional information for you.
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