Let's help by getting some clarity first.
You received two W-2 's from the Census Bureau with the same amount, lets say 1,000. Does that mean you made 1,000 twice? OR that both W-2 's are reporting the SAME 1,000?
I'm guessing you did census work in both Delaware and Pennsylvania? Or was this work you did for the Census Bureau remotely?
If Pennsylvania / Philadelphia tax was withheld and shouldn't have been, you can file a Pennsylvania and Philadelphia return to get the tax refunded.
It is unclear id the proper DE tax was withheld.
It is too late for the employer to change how the state tax was withheld and paid, not too late for an employer to issue a CORRECTED W-2.
Were your W-2's REPORTED correctly?
Do they show what really transpired?
Did you earn both incomes?
Were each incomes taxed by different states?
Should both incomes been taxed by the same state?
When you filed the Delaware state tax return, did you pay tax on both (all) income?
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