Whren, reasonable suspicion, and consent to search.
Connecticut courts apply both the U.S. Constitution and the Connecticut Constitution to traffic stops & pretext claims. When state protections are broader than federal ones, Connecticut judges follow the state rule. When they are equal or narrower, federal precedent controls under the Supremacy Clause.
Federal cases governing traffic stops & pretext include controlling U.S. Supreme Court decisions and binding precedent from the federal circuit covering Connecticut. Civil remedies most often proceed under 42 U.S.C. § 1983, with defenses including qualified immunity.
Legal information, not legal advice. For advice on your situation, consult a licensed attorney in Connecticut.