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State tax filing
Q. Also, generally, if you pay the tax to one state, does the other state (state 2) generally exempt you of any tax on that income?
A. Technically, no. But, because of the "other state credit", effectively yes. Or, more accurately, partially yes. See next question.
Q. Or do you end up still owing some money to your home state because they do their own calculations?
A. Maybe. It depends on the calculations. Pennsylvania has a single-rate income tax of 3.07%, while West Virginia uses a progressive, multi-bracket system with rates ranging from 2.22% to 4.82% . So, depending on where you fall, on the WV brackets, the PA credit may not be enough to cover the full WV tax. Also, the credit is limited to the amount of WV tax calculated on the PA source income. So, for example if the PA tax is 3.07%, but WV only taxes you at 2.22%, WV will not give you credit for the full amount of PA tax paid. The simplified calculation is 2.22/3.07 = 0.72; WV would only give you credit for 72% of the PA tax paid.