Yes, in most cases. Connecticut follows modified comparative fault under Conn. Gen. Stat. § 52-572h, so being partly responsible reduces your compensation rather than eliminating it. Your award is cut by your percentage of fault, but if your share is more than 50 percent you may not recover at all.
Partial fault is not the end of a claim
Many people assume that any responsibility for an accident ends their claim. In Connecticut it does not. The question is how much responsibility, and the dividing line is 50 percent.
What the reduction looks like
If the total damages are set at a given amount and the injured person is found 30 percent responsible, the recoverable amount is reduced by that 30 percent. The claim continues; the number changes.
The deadline still applies
Comparative fault affects how much can be recovered, not how long you have to file. Most Connecticut injury claims must be brought within two years under Conn. Gen. Stat. § 52-584, and in most cases no more than three years from the act or omission complained of, even if the injury is discovered later.