Credit for taxes paid to another state
A credit on your resident return for income tax another state charged on the same income, which removes double taxation but is capped at what your home state would have charged on that income.
Every state that taxes wages offers one, because without it the combination of resident taxation on worldwide income and source taxation on in-state income would tax cross-border commuters twice over. It is claimed on the resident return, which is why the nonresident return has to be completed first: its tax figure is an input.
The cap is where money is lost, and it is widely misunderstood. The credit is limited to the home state's own tax on that same slice of income. If the work state taxes it more heavily, the excess is not refunded by either state — so the effective rate on cross-border income is the higher of the two, not the lower and not an average.
A resident of a state with no income tax has no resident return, and therefore no credit. That is why the convenience-of-the-employer rule bites hardest on people who move somewhere with no income tax while keeping an employer that has one.
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What is credit for taxes paid to another state?
A credit on your resident return for income tax another state charged on the same income, which removes double taxation but is capped at what your home state would have charged on that income.