Simple answer: Yes, select multiple states (or "more than one state" on desktop software).
If your mutual fund did not provide a breakdown*, you check the box “I earned tax exempt dividends in more than one state” ("Multiple States" in the online program) on the first screen after entering the 1099-INT or 1099-DIV. Then select "More than one state" at the bottom of the state scroll down list.
If your mutual fund company provided you a breakdown, you are only interested in your home state**. Multiply the % for your state by your total tax exempt dividends to get a $ amount (you can't enter the % in TurboTax [TT]). When asked which state, check the box "I earned tax exempt dividends in more than one state". In the drop down menu, select your state and enter the $ amount you calculated. In the 2nd box, select "More than one state" (at the bottom of the scroll down list) and enter the remaining dollar amount.
*Most mutual funds will provide a breakdown. But you usually have to ask for it, or find it on their web site.
**Your state will tax all the dividends except the dividends from municipal bonds from your state and US Territories.
Screen shot at https://ttlc.intuit.com/community/state-taxes/discussion/re-exempt-interest-dividends-are-entered-fr...
