Conn. Gen. Stat. § 53-258a: Misuse or mutilation of the flag.

Any person who, in any manner for exhibition or display, puts or causes to be placed any inscription, picture, design, device, symbol, name, advertisement, word, character, mark or notice upon any flag, standard, color or ensign of the United States or the state flag of this state or any ensign evidently purporting to be either of such flags, standards, colors or ensigns or in any manner appends, annexes or affixes to any such flag, standard, color or ensign, any inscription, picture, design, device, symbol, name, advertisement, word, mark, notice or token or displays or exhibits or causes to be placed or exhibited any flag, standard, color or ensign of the United States or the flag of this state or any flag, standard, color or ensign evidently purporting to be either of such flags, standards, colors or ensigns, upon which in any manner is put, attached, annexed or affixed any inscription, picture, design, device, symbol, name, advertisement, word, mark, notice or token or publicly misuses, mutilates, tramples upon or otherwise defaces or defiles or puts indignity upon any of such flags, standards, colors or ensigns, whether any of such flags, standards, colors or ensigns are public or private property, shall be guilty of a class A misdemeanor. Flags, standards, colors or ensigns, the property of or used in the service of the United States or of this state, may have inscriptions, names of actions, words, marks or symbols which are placed thereon pursuant to law or authorized regulations.