It's Sunday, so it's church record day.
The Connecticut State Library is home to the Church Record Index. Made up of slips detailing each record, the Church Record Index is organized by name and then date. It is far from complete. It contains records for only around 150 churches, mostly Congregational churches. Records are limited in scope as well. The most recent date from the early 20th century. Despite its failings, the Church Record Index can be a good place to start if you don't know where to look for your ancestors' records. Find out more at http://www.cslib.org/church.htm.
The Boston University School of Theology archives hold records from many Connecticut methodist churches. While these records have yet to be digitalized, the online finding aid can provide you an idea of what may be found at BU. If you're looking for information on the early records of the methodist church in East Thompson, the archives may be what you need. Those records are missing after 1900. Take a look at their records at http://www.bu.edu/sthlibrary/archives/collections/neccah/records-files-state/ct-records/.
Good luck with your research!