Fiddlesticks. We know he did die there, because the date and place showed up in a reliable cemetery listing and in a family prayer book, not to mention death notices in his hometown newspaper.
I have other research to pursue, so I joined the CT Society of Genealogists.*
When the blue membership card arrived, I took myself down to town hall, smiled sweetly, flashed the magic card, and presto! I got into the vault and found the ancestor's name, in black and white, listed in the town's death index (and the only person of that last name to die that year, by the way).
Then I turned to the death cert in the book of bound death certs. Alas, all this effort for very little. No name of father or mother, no town of birth, not even the spouse's name (which we know anyway). Just death date, place, name of doctor, name of undertaker, and name of embalmer (TMI).
But now we KNOW for sure where and when, which is something.
Next stop: The main library in the town where this man lived for decades, and the vital records area. So many ancestors, so little time!
*2022 update: The town clerk in Manchester, CT, lists the membership cards that are acceptable as proof that someone is accessing records for a legitimate genealogical purpose.