In order to close a trust, in other words disolve the trust, where you have cotrustees, and they are still alive, then it would take both signatures assuming the trust was revocable; however a cotrustee of an irrevocable trust could file a petition into probate court, with consent of the beneficiaries to close the trust, and the court would probably order the disolving of the trust , unless the cotrustee father could raise a valid objection.