A Personnel Committee, consisting of the Mayor and two (2) Council members appointed by the Council President, such appointments being subject to approval of Council, is established by this Charter. The Personnel Committee shall, when a vacancy exists for the office of City Manager, City Finance Director or City Law Director due to death, resignation, or removal, investigate and subsequently recommend in writing one (1) or more suitable persons for appointment. The members of the Personnel Committee shall select one (1) of its members as chairperson. All recommendations of the Personnel Committee shall be presented by the Mayor to Council as a whole.