The CT cops usually around Fairfield County has nothing to do but bully the innocent civilians. The state trooper are another parasites. Your situation seems weather related, usually in the insurance there is a clause like comprehensive, which protects you from things like accident like snow, ice, rain or other mother nature damages, meaning it's no one's fault but mother nature cause. There will be a deductible depending on your choice(e.g 0, 250, 500, 1000 etc.).
You should plea not guilty and go to court and fight for it, since speeding ticket seems a joke. trooper should have a video for that too(as a proof). You should hire an attorney. If you live around Fairfield County( from Stamford- Bridgeport, Stratford), I know a very good lawyer, he can help you. send me your email address, I will send you his info. good luck