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The state of New York follows the federal in that IRA distributions prior to retirement are taxable and added to your income.
The amount, used to compute federal adjusted gross income, is the amount from which New York taxpayers begin to figure state taxes. There is a NY exclusion up to $20,000 on retirement but not until after 59 1/2.
New York's personal income tax system consists of eight brackets and a top rate of 8.82%. Your rate will depend on your taxable income for the year.
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I cannot calculate tax for NY without knowing dollar amounts for your income and the 401k