Given your self-described circumstances, no, you don't have to pay taxes to Vermont on your interest income. However, since your husband works in Vermont, you will have to file a Vermont state tax return there, and pay Vermont taxes on his wage income. Of course, you'll also have a New York state tax return (and federal tax return) too.
The interest income question is quite straightforward, and how you can answer it in TurboTax (Vermont nonresident state module) is illustrated in the screen-capture image below.
For your husband's wage income, it will be taxable by both Vermont (since he physically works there) and by New York (since that is your state of residency). But, you should then also be allowed a state tax credit for the taxes paid to Vermont on this "double-taxed" state income.
Perhaps you're familiar with how that process works, or perhaps you are not. As a quick refresher, though, that's what typically happens when someone lives in one state, yet works in another state, and both states have a personal income tax. The worker ends up reporting (and paying) taxes to both states on that same wage income, but then is generally allowed a tax credit from one state to apply toward the taxes of the other state . . . thus either reducing or eliminating the double-taxation. Confusing? Yes; but that's how the system is designed.
In the New York / Vermont pairing, specifically, if you look closely at your New York Form IT-201, after you're done preparing your tax return, and when done correctly in TurboTax, the amount of state taxes paid to Vermont on the nonresident return Form IN-111, should appear a counter-acting state taxes paid credit (called a "resident credit" by New York), on Line 41 of the New York IT-201. In other words, New York will allow the entire Vermont state taxes paid amount as a credit toward your New York state tax liability.
Finally, here's an important tip. In the TurboTax software, in order for the program to work properly and the state credits to flow to where they need to go, there is a specific tax preparation sequence that needs to be followed; it goes like this. Do your federal return first (error check, then complete); fill out your nonresident state return second (Vermont, in this instance); and then finish with your home state return last (New York, in your case). If you ever get out-of-sequence, then it is advised that you delete all your state returns and begin to pick up the preparation process again at the end of the federal return (deleting states won't affect federal). This should ensure that the state credits are properly applied by TurboTax.
If you have further
questions, encounter any difficulties, or just want to speak with a live tax
expert who can walk you through your TurboTax entries (including the ability to
screen-share with your computer), please feel free to contact us. We
would be happy to help you (and as a paying customer, the call is free to
you). Here is a link where you can create a support ticket and reach us:
https://support.turbotax.intuit.com/contact/
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