Box 10 should tell you which state. If not identified you might contact the payer, NY DOL, to inquire. Most likely it is NY. Also, to correct my previous post, it does appear that NY does tax non-residents on unemployment benefits that are related to NY wages. So you should file a NY non-resident return to report those payments and any taxes withheld on that income.
In the "My Info" section at the bottom you will indicate you earned income from another state and select NY. You will allocate your 1099G income to NY. At the end of the NY interview take note of the income and taxes paid to NY as those numbers can be used to claim a credit on your VT resident return for taxes paid to another state to mitigate the double taxation.
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