Connecticut has 8 counties, which each have their own trial courts. The Appeals Court of Connecticut reviews the decisions of those lower courts. If further appellate review is desired it is handled by the Supreme Court of Connecticut.
The three largest municipalities in Connecticut are Bridgeport, New Haven, and Hartford.
Any complaints regarding the competency or ethics of your attorney should be made with the Office of Chief Disciplinary Counsel. To report an attorney mail a Connecticut Complaint Form to 287 Main Street, Suite 2, Second Floor, East Hartford, CT 06118-1885.