I have always lived and worked remotely for my company, and I never travel to work there or have the option to work there. There are two states on my W-2, but I don't think I have any tax liability to the nonresident state. I asked them to correct my W-2, but they said they couldn't, and then added that my wages were reported to the IRS and my resident state only, what does that mean? That I don't need to file a nonresident return?
I haven't had anything withheld from either state so I am not worried about that. It will just cost me an extra $300 for the nonresident state, even with a credit on my resident state return.
You do not have to file a return for the nonresident state because you didn't live or work there. All the income as a remote employee is only taxable in your resident state. If you've started a return for this state, delete it.
I suggest that you leave off the entries in your W-2 for the nonresident state. If your employer reported State Wages for that state in box 16, then they certainly should issue a corrected W-2. It's not true that they "couldn't". If it just has the state name but the rest is blank, there's no real reason they would need to correct the W-2. They are saying they only reported the wages to your resident state, which is reassuring, but making an entry for state wages to the other state is wrong.
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