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As a resident of Pennsylvaniia who works in Delaware, you would be required to file a non-resident return with Delaware (Form 200-02). You would be allowed a credit on your Pennsylvania return for taxes imposed by Delaware. Your employer would be required to withhold Delaware taxes as long as you work in Delaware.
You have to pay PA income tax on income earned in PA & DE tax on income you earned in DE.
As a PA resident you get credit for taxes paid to DE from your PA tax liability.
If you had no income in PA then you still file a PA resident return and you will get 100% credit for taxes paid to DE,
You will file a DE non-resident return and report 100% of your Federal Income & adjustments in Col 1 Page 2 and your income from DE sources in Col 2 Page 2.
Each state wants their 'pound of flesh' from income earned in that state.
Ultimately you will pay DE tax on income earned there and PA tax on income earned there.
Here are some links to the DE forms you will need:
No problem. We are here to help. You don't get a credit for the total liability but on the taxes actually paid which is usually an amount equal to any withholding from your paychecks.
Box 17 of your W-2 is where you will find the amount of taxes paid to DE. That is the amount for which you will get credit on your PA return.
If my answer is not clear then let me know what are the state taxes you paid to each state (find those amounts in Box 17 of your W-2) I will attempt to be more specific.