Exemption certificate
The form an employee gives their employer to stop a state withholding from their wages — most often because a reciprocity agreement or a statutory nonresident exemption applies.
It goes to payroll, not to a revenue department, and it belongs to the state where the work is performed. That is the detail people get backwards: a Pennsylvania resident working in New Jersey files New Jersey's Form NJ-165, and a New Jersey resident working in Pennsylvania files Pennsylvania's Form REV-419.
It is not retroactive. Tax already withheld before the certificate was filed comes back only by filing a nonresident return for that year and claiming a refund. Some states also require the certificate to be renewed annually — Virginia and Minnesota both do — while others, Pennsylvania among them, treat it as standing until the employee's state of residence changes.
The District of Columbia's Form D-4A works the same way mechanically but rests on a different footing: the District is barred from taxing nonresidents at all, so the certificate reaches residents of every state rather than a named partner list.
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In one sentence
What is exemption certificate?
The form an employee gives their employer to stop a state withholding from their wages — most often because a reciprocity agreement or a statutory nonresident exemption applies.