If, by reason of an equal number of votes having been cast for 2 or more persons for the office of Senator or Representative in the General Assembly, clerk of the peace, register of wills, recorder, levy court commissioner, receiver of taxes and county treasurer, sheriff, county executive or county council member, it appears to the Court that a vacancy will occur in the office, a certificate of such fact shall thereupon be made under the hands of the Court, and under its seal, which certificate shall be transmitted by the Court to the Governor, and such certificate shall be delivered as provided in § 5709 of this title.