Conn. Gen. Stat. § 47-55: Damage by animals.

All damage done within enclosures by cattle, horses, asses, mules, sheep, swine or goats, when the fence is sufficient, shall be paid by the owner of the animals. No person shall recover for damage done within his enclosure by reason of the insufficiency of his fence, unless done by animals at large contrary to law, or by unruly cattle that are not restrained by ordinary fences; or unless the owner of animals puts them into or voluntarily trespasses on such enclosure; or unless they entered through a part of the fence which was sufficient; in all of which cases the owner of the land may impound them and recover poundage and damages.