No, not necessarily. Your resident state taxes all of your income, including income sourced to another state. Each state has its own rules and tax laws. MA does not give a dollar for dollar credit for taxes paid to another state.
Filing Tax Returns in Multiple States - If your nonresident state has higher taxes than your resident state, you might end up paying more in total taxes because your resident state won't allow you a full credit. This is common for MA residents that work in CT. The linked article has more information on how states calculate your tax bill, but rest assured, TurboTax is following the tax code for each state.
MA credit for taxes paid to another state
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