My 1099-DIV doesn't have a state listed for exempt-interest dividends. I have multiple investments in this account. What should I use in Select State box?

Simply leave "State" box empty.

 

"Boxes 14–16. State Information These boxes, and Copies 1 and 2, are provided for your convenience only and need not be completed for the IRS. If you withheld state income taxes on this payment, use the state information boxes to report payments for up to two states."

 

Thus, if not required to be completed for the IRS, then you are not required to list anything if nothing is listed.

 

IRS Pub. Instructions for Form 1099-DIV (pg. 5)