Conn. Gen. Stat. § 52-477: Permanent injunction; stay pending appeal.

When judgment has been rendered for a permanent injunction ordering either party to perform any act, the court, upon an application similar to that mentioned in section 52-476, shall stay the operation of such injunction until a final decision in the court having jurisdiction, unless the court is of the opinion that great and irreparable injury will be done by such stay or that such application was made only for delay and not in good faith.