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State tax issues for NJ resident with DC tax withheld, and likely refunded
If you already filed the DC return, you can try and wait with filing the NJ return until you get the answer from DC.  You can file an extension request with the NJ division of taxation here. Or, you can file without claiming the credit, and worst case amend later and claim it if DC refuse to refund. I find it highly unlikely that DC will decide that a person staying for a couple of months over the year in hotels will count as a resident.