No, you cannot insure a car with a salvage title in Connecticut. Salvage vehicles are cars that have been declared a total loss, meaning they're too damaged to be worth repairing and cannot be driven legally. As a result, no legitimate car insurance company writes policies for them.
Although insurance companies in Connecticut won't insure a car with a current salvage title, you can get coverage if you have the vehicle repaired and inspected by a state-certified mechanic. If it's declared safe to drive, the DMV will issue the car a rebuilt title. Several insurance companies, including Allstate and Geico, sell policies to vehicles with a rebuilt title.
Keep in mind that some insurers will only sell liability insurance for rebuilt cars, meaning that they won't pay for any physical damage to the vehicle. Even if you are able to get collision and comprehensive insurance, your policy may not cover the full value of the car if it's totaled again.