Md. Code, Elec. Law § 8-602

(a) (1) (i) If there is a vacancy in the office of United States Senator, the Governor shall appoint an eligible individual to fill the vacancy as provided in this paragraph. (ii) The Governor shall appoint one of three individuals whose names are submitted to the Governor in writing, within 30 days after the occurrence of the vacancy, by the State Central Committee of the political party, if any, with which the vacating Senator had been affiliated at the time of the Senator’s last election or appointment. (iii) Each individual whose name is submitted to the Governor must have been a registered voter affiliated with the political party of the vacating Senator on the date immediately preceding the date on which the vacancy occurred. (iv) The Governor shall make the appointment within 15 days after names are submitted by the State Central Committee of the appropriate political party. (v) If names are not submitted by the State Central Committee of the appropriate political party within 30 days after the occurrence of the vacancy, the Governor shall appoint within another period of 15 days any qualified individual who was a registered voter affiliated with the political party of the vacating Senator on the date immediately preceding the date on which the vacancy occurred. (vi) If the vacating Senator was not affiliated with a political party at the time of the Senator’s last election or appointment, the Governor shall appoint any qualified individual within 15 days after the occurrence of the vacancy. (2) Except as provided in paragraph (3) of this subsection, the appointed individual shall serve until a successor is elected pursuant to subsection (b) of this section to fill the remainder of the term. (3) The appointed individual shall serve for the remainder of the term if the vacancy occurs after the date that is 21 days before the deadline for filing certificates of candidacy for the election that is held in the fourth year of the term. (b) If the vacancy occurs on or before the date that is 21 days before the deadline for filing certificates of candidacy for the next succeeding regular statewide election, the Governor shall issue a proclamation immediately after the occurrence of the vacancy declaring that a special primary election and a special general election shall be held at the same time as the next regular statewide primary election and regular statewide general election.