how do I find out about the interest on out of state municipal obligations acquired after December 31 2011.

where are you being asked for this is this some particular state requirement for specific treatment of muni bonds based on that acquisition date, some sort of state tax law change?  that date is close to the date that 'covered' securities were introduced for 1099-B reporting at federal level, but doesn't quite line up for bonds which was Jan 1 2014 onwards.

either way if this is needed for some reason - your 1099-INT won't list the acquisition date, the only place you might see it is on 1099-B for a covered sale.  You would need to go back to your own records for that, some brokers in the online account you can bring up the lot details with acquisition dates, or brokerage statements.