Conn. Gen. Stat. § 54-63e: Bond or promise conditioned on appearance.

Whenever any arrested person is released upon his written promise to appear or upon bond without or with surety, such promise or bond shall be conditioned that he shall appear before the Superior Court. Any promise or bond without or with surety, and any fee paid for a bond with surety, shall also cover any appearance of such person, unless modified, and if modified any such fee which has been paid shall be credited toward the fee of any increased or new bond with surety.