Assuming you actually work in VT, see this:
http://tax.vermont.gov/individuals/income-tax-returns/who-needs-to-file/nonresident
You will then file a resident return in NY, and get credit for most or all of the taxes paid to VT. But you may still owe NY some money, due to the difference in tax rates between the two states, or if you have other, nonwage income.
