(a) A custodian of local government records shall, at the expiration of the custodian's term of office, appointment, or employment, deliver to the custodian's successor, if there is one, all local government records in custody. If there is no successor, the governing body shall determine which officer of the local government shall have custody.
(b) If the functions of an office of one local government are assumed by another local government, the governing bodies of the two local governments shall determine in which local government custody of the records of the office shall be vested.