My W2 lists two versions of wages and income tax. One for New York and one for "TOTAL STATE". I did not work/live in New York for all of last year. Is this wrong?

Yes, you should reach out to your employer. However, if your employer is in New York (NY), then see the information next.  If you do file the NY return you will qualify for credit for taxes paid to another state on the same income for your resident state.  It's not clear if you do live in NY.  If it's New York City (NYC) only that is an issue, you should speak to your employer.

 

If you do live in NY state you can ignore the following information.

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 You must file Form IT-203, Nonresident and Part-Year Resident Income Tax Return, if you:

• were not a resident of New York State and received income during the tax year from New York State sources, or
• moved into or out of New York State during the tax year.

Your working days should not include weekends or vacation days if you did not work. 

 

If you are a New York State nonresident you must file Form IT-203, Nonresident and Part-Year Resident Income Tax Return, if you meet any of the following conditions:

• You are a nonresident with New York source income and your New York adjusted gross income Federal amount column (Form IT-203, line 31) exceeds your New York standard deduction.
• You want to claim a refund of any New York State, New York City, or Yonkers income taxes withheld from your pay.
• You want to claim any of the refundable or carryover credits available.
• You had a net operating loss for New York State personal income tax purposes for the tax year, without having a similar net operating loss for federal income tax purposes.