(a) The clerk of the peace shall furnish to any justice of the peace in his or her county, upon payment of the fee to the State, as many marriage licenses as the justice may desire. No person other than such clerk of the peace or justice shall dispense or distribute the licenses. The clerk of the peace, upon dispensing such marriage license, shall notify the State Registrar of Vital Statistics, as provided by law.
(b) This section shall not apply to the clerk of the peace of New Castle County.