-- Federal court records are kept at the court. Some of the federal records are then moved to the regional archive -- i.e., U.S. District Court for the District of Connecticut records, if moved, will be found at the Northeast Region-Boston Federal Records Center in Waltham, MA (this is part of the National Archives).
-- Appeals from the U.S. District Court for the District of Connecticut go to the U.S. Court of Appeals for the Second Circuit with the archived records being located at the National Archives at New York City.
-- Much material filed in federal cases since around 2005 (and in some cases earlier) is available for a fee from the federal government's PACER.
Start by reviewing the following PDF on records retention rules for Connecticut towns:
Also consult the Open Government Guide Connecticut from the Reporters Committee for Freedom of the Press:
State records will be found at the Connecticut State Library and Archives. As a starting point, you should consult the finding aids that are available at the following link: