Most records in CT are kept at the town level, but you won't find many official birth, marriage or death records going back to 1840. Estate records will usually be found at the local Probate Court. The state archives have many early church records. I believe most of these are also available on Ancestry.com.
I would suggest you call the town clerk in each of the towns you are interested in to find out what records they have.
This page on the state archives website gives more info about their holdings:http://www.ctstatelibrary.org/topics/history-genealogy