Interest income is taxable in the state you lived in when you received it.
NY calculates what your New York tax would have been if you earned everything in NY, then determine the percentage of your income that is subject to New York State tax and the amount of tax apportioned to New York State.
Check line 45 on form IT-203 to see how New York computes the percentage of income taxed within New York.
If you were a resident of New York State for only part of the tax year, you must pay New York State tax on all income you received while you were a resident of the state and on income you received from New York State sources while you were a nonresident.
Form IT-203 instructions.
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