Conn. Gen. Stat. § 14-293a: Riding animals on highways.

Any person who rides any horse or other animal upon a public highway shall conform to the provisions of this chapter and chapter 249, unless such provisions clearly do not apply from the language or context or such application would be inconsistent with the manifest intention of the statutes. The fines established in accordance with section 51-164m for violations of the provisions of this chapter and chapter 249, with respect to a motor vehicle, shall apply if the same violation of a provision is committed in the riding of a horse or other animal.