I am being asked "Which state is $XX.XX of exempt-interest dividends from?" Where can I find this information on the tax form?

That information would be reported on supplemental statements attached to your form 1099 that reported the income. If not, then you would have to ask the issuer of the form. It is asked to see if the interest is from state obligations of the state that you live in, as it may get special tax treatment there. There may be a response available that says "various" that you could use as a default answer.

@bsymesjr 

Unless you are willing to go thru the calculation to break out JUST the amount from your own state's bonds, you would select "Multiple States" for all of it

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IF you are going to break out your own state's $$ then you check the selection that displays the extra boxes

(note, for a 1099-DIV, box 11, this is not allowed by Illinois, and CA & MN have severe restrictions on when it is allowed).  The amount actually from your own state's bonds would have to be more than ~$50 or $100 before it had much of an effect.

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Example is for a NC resident: