Because the Congregational Church was the “state church” of Connecticut until the Constitution of 1818, many Connecticut ancestors were Congregational by default. As a result, Congregational Church records should be part of your search.
In the early 20th century, the Connecticut State Library began a project to preserve church records. They asked churches to submit their older records and made a photostat copy of each book. In some cases, the Library retained the originals and returned the photostat; in other cases, they did the opposite. The bulk of churches that participated were Congregational. The full list can be found here.
Approximately 25% of these records were indexed and abstracted into the Connecticut Church Records Abstract collection. Those not indexed were still microfilmed. Digital images of that microfilm can be found on FamilySearch, typically through the catalog search.
If you do not find your ancestor listed, it’s important to confirm that you haven’t missed a church. While the Congregational Church is well represented in the State Library’s collection, the collection does not include every Congregational church in the state. Some still have their records available only onsite.
Connecticut Roots by Charter Oak Genealogy 
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