(a) The clerk of the peace shall, within 10 days after the appointment by the government of his or her county of any constable, send by mail to the Auditor of Accounts a true certificate of the name of every such constable, stating therein who is, and who is not, liable to the payment of a fee of $5.00, according to law.
(b) This section shall not apply to the clerk of the peace of New Castle County.