Conn. Gen. Stat. § 52-476: Continuance pending appeal.

When a temporary injunction has been granted and upon final hearing judgment has been rendered adverse to its continuance, either party may apply to the court rendering the judgment, representing that he intends to appeal the case to the court having jurisdiction and praying that the temporary injunction may be continued until the final decision therein. Unless the court is of the opinion that great and irreparable injury will be done by the further continuance of the injunction, or that the application was made only for delay and not in good faith, the court shall continue the injunction until a final decision is rendered in the court having jurisdiction.