How do I find out what state my exempt interest dividend is from?

Percent of tax exempt holdings for each state is generally in the brokerage statement you received. You could also ask your broker or research it online. 

You get that from your mutual fund company. If they 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.

If you can't find the breakdown (or you don't want to make the effort to look); it's no big deal. The percentage for any particular state is usually small.  Here's Fidelity's (for an example). https://www.fidelity.com/bin-public/060_www_fidelity_com/documents/taxes/2023-tei-by-year.pdf

California, and Minnesota require that the bond fund hold at least 50% of the fund's holdings be in their own state's bonds, before you can break out that state's $$ for possible lower state taxation.  Illinois, essentially,  doesn't allow it at all.

Generally, it isn't worth the effort to break out you own state's bond $$, unless your State's bond $$ ends up being more than somewhere in the $50-$100 range 

So if you don't want to mess with it, it is perfectly acceptable to assign the entire $$ amount to the single designation of "Multiple States"