When I stumbled across Bashan in a Family History Library listing for a cemetery transcription, I was shocked. I'd never heard of Bashan - or of the cemetery referenced. A little digging on Google and the "Connecticut Unique Place Names" page told me why. Bashan is part of Moodus, which is part of East Haddam. And the cemetery... It's called Bashan Lake and is listed on Find A Grave.
Lesson learned. If you don't find the town in your first search, make sure you check the "Unique Places Names" list. You're probably looking for a village in a larger town. And you'll need the larger town name to find records.