Conn. Gen. Stat. § 45a-430: (Formerly Sec. 45-271f). When distributees to give security for contingent or future debts.

Each person to whom any part of an estate is distributed or paid by order of the Court of Probate and each person to whom any property is devised or bequeathed when no sufficient provision has been made by the will for the payment of the debts out of some particular property shall, upon the request of any person having a claim against the estate, contingent or not yet matured, give a bond to the state, with surety to the acceptance of the Court of Probate. The bond shall stipulate that if, after the settlement of the estate, debts appear and are allowed, such person will pay to the fiduciary his proportional part of such debts and of the charges of the fiduciary.