State tax filing

No.  It would be the state that your fund invested in to get the tax exempt dividends.  

In all likelihood, the dividends truly are from more than one state, so you are going to want to select "More than One State" - see screenshot below.  But its possible you can get a tax benefit on your state return if you can identify which state the dividends are from.  The tax benefit you would get would be that your home state would not tax the dividends that come from your state, if there even are any (i.e if the fund invested in California municipal bonds and you are a resident of California, then those dividends would be tax exempt on your state return).  They would still tax the other dividends.

This information would only come from your financial institution.  If it is not listed right on the 1099DIV (which it often is not), then you would need to contact your broker or financial institution for more information about the funds investments.  It might be listed in your year-end reports or a prospectus online.    

Also, you can not worry about trying to find the information and just select more than one state and continue if you: 

 - Live in a state with no income tax (AK, FL, NV, SD, WA, WY)
 - Live where exempt-interest dividends from other states aren't taxed (District of Columbia, IN)
 - Have a small amount of exempt-dividends and aren't concerned with extra state tax. Your state will tax these dividends if you don't live in an area listed above.