There is a series of books, The Public Record of the Colony [State] of Connecticut. These books contain transcriptions of various public records. Many of the volumes can be found as digital files online; a listing is included at the end of this post. Following are four examples of what can be found in these books.
This is a (partial) list of Assembly members that took the Oath of Fidelity in August 1777, taken from the book, The Public Records of the State of Connecticut From October 1776 to February 1778 (p. 378; the rest of the list is on page 379).
This excerpt related to the will of Lieutenant Robert Webster in May 1677, taken from the book, The Public Records of the Colony of Connecticut From 1665-1678 (p. 310).
This is a list of Freemen on the “South side of Hartford, 1669, Octo.,” , taken from the book, The Public Records of the Colony of Connecticut From 1665-1678 (p. 518).
This excerpt has to do with the dividing line between Preston and New London in May 1702, , taken from the book, The Public Records of the Colony of Connecticut From August 1689 to May 1706 (p. 384).
I was able to find many of the volumes online through either Internet Archive or Google Books. Following is a list of those I was able to find, with a link to the book. They are also available at Ancestry here.