I think the challenge will increase with the length of time the theatre's been closed.
The property owner would probably know a lot about its final days, especially if he/she ran it personally. Still, try to get any info from the last operator backed up by a second source, as they may have a chip on their shoulder from the closing.
The city/county might also know some things, especially if the closing was due to anything surrounding codes... structural condition, etc.
Check in with the local paper. The theatre was probably a regular advertiser. Whether they ran ads for each day the theatre was open or just on the busy weekend days might say something.
If the place hasn't been closed too long, have a booker check with the studios. They might have records about the theatre's past performance, though some of them don't have that information readily available after a couple years or so, and getting them to dig will probably depend on who you (or your booker) know(s).
Finally, take anything you don't get on paper with a huge grain of salt. Memories can be colored by how the community feels about a reopening. A mediocre place could be fondly remembered as a boxoffice powerhouse by a city official who wishes it was open again (possibly generating local tax revenue)... or a totally useless dump by someone who might have been tossed for one reason or another.
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