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Hi and welcome to our site!Unfortunately - because that severance payment is related to work done in NY - it is considered as income from NY sources - and as such is taxable for NY.In general state income tax liabilities are based on both - residency and source of income.Even you will be nonresident of NY in 2014 - that income will be taxable on the state level because it is a compensation for services performed in New York State.See for reference - http://www.tax.ny.gov/pubs_and_bulls/tg_bulletins/pit/ny_source_income_nonresident.htmYou will be required to file your tax return as a nonresident - and only income from NY sources will be subject of NY state income tax.
Most likely - your employer will have withholding out of your severance payment - and most likely - you will claim a partial refund on your tax return. You should file Form IT-203, Nonresident and Part-Year Resident Income Tax Return - http://www.tax.ny.gov/pdf/current_forms/it/it203_fill_in.pdfHere are instructions - http://www.tax.ny.gov/pdf/current_forms/it/it203i.pdf