(a) in the case of a county, to the board of supervisors thereof, except when the county has a county executive, county president, county manager or other officer or board authorized to appoint heads of administrative departments or the chief executive officer of the social services department, in which case it shall mean such executive, president, manager, other officer or board;
(b) in the case of a city, to the mayor, manager, other officer, or the board having authority to appoint department heads or the chief executive officer of the social services department.