Conn. Gen. Stat. § 29-6a
Use of official hat and insignia of state police.
(b) Thereafter, no policeman shall wear or use in public such official hat or insignia, or any imitation, reproduction or facsimile thereof, except a duly appointed member of the Division of State Police within the Department of Emergency Services and Public Protection authorized by the Commissioner of Emergency Services and Public Protection to wear such hat or insignia.
(c) Any person who violates the provisions of this section shall be fined not more than two hundred fifty dollars.