Trying to sort out which Connecticut church holds your ancestors' records can feel almost impossible. In a large city, there can be as many as six or more churches. Each could, in theory, be the right place. But where do you look?
Although they set out to chart the history of their own church, members of St. John in Middletown have helped provide a guide: http://saintjohnchurchmiddletown.com/aboutus.aspx. Their webpage, entitled "our history," traces Roman Catholics in Connecticut from 1823 through the 1900s. The focus is primarily upon St. John's Church and how it has changed over the centuries. However, this website includes a detailed section on clergy appointments to central Connecticut before the construction of their first church in 1845. This information is quite helpful. If your ancestor was Catholic and from Connecticut, you now know that you may need to look in Boston to find their records.
More detail would be helpful, but this is a good start.