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I was a graduate student last year for an American university, but spent the whole year in Italy doing research with collaborators without holding any residence in the US. I'm not a US citizen and for last year I'm also a nonresident for tax purposes to the IRS.

When I did my change of address to the university it seems like this was never communicated to payroll, which seems to have kept my local address on file and therefore deducted state taxes for Pennsylvania as well as local taxes from my pay even though I wasn't there for the whole time and could under no circumstance could be considered a resident of Pennsylvania.

Since my employer was located in Philadelphia, I'm wondering if I should have had to pay any state and local taxes at all?

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Guidance from Pennsylvania's Department of Revenue states (on page 11) that

Nonresidents are taxed on the following types of income derived from sources within Pennsylvania.

Compensation Pennsylvania taxes nonresidents on compensation for services performed in Pennsylvania unless the taxpayer is a resident of one of the reciprocal agreement states.

Accordingly, it appears that compensation from Pennsylvania sources (your university) to non-residents for services performed outside of Pennsylvania are not part of taxable income for Pennsylvania.

In order to follow @littleadv's advice to "claim refund" for the amounts withheld, you should file form PA-Schedule NRH along with form PA-40 to make clear that the number of working days you spent in Pennsylvania was 0, thus making the wages earned while abroad excludable from PA's income tax.

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You should file a tax return in PA, and if you're considered non-resident - claim refund for these amounts.

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