(a)

1. (1) If there is a vacancy in the representation from this state in the House of Representatives in the Congress of the United States, the Governor shall, within five days after the fact comes to his or her knowledge, issue a proclamation setting dates for a special general election that is not less than 84 nor more than 120 days from the date of the vacancy and requiring nomination of candidates as provided in §3-10-4(a)(2) of this code: Provided, That no such proclamation may be made nor may a special election be held if the vacancy occurs after the 84th day prior to the regularly scheduled general election for a new full term of the office. The election shall follow the requirements of §3-10-1 of this code that are not in conflict with this section.
2. (2) The party executive committees for the congressional district for which there is a vacancy shall each, within 30 days of the Governor's proclamation, nominate a candidate to stand at the general election required by §3-10-4(a)(1) of this code.

(b) If there is a vacancy in the representation from this state in the Senate of the United States Congress, the vacancy shall be filled by the Governor of the state by appointment. The Governor shall make the appointment from a list of three legally qualified persons submitted by the party executive committee of the same political party with which the person holding the office immediately preceding the vacancy was affiliated at the time of the previous election for that office. The list of qualified persons to fill the vacancy shall be submitted to the Governor within 15 days after the vacancy occurs, and the Governor shall duly make his or her appointment to fill the vacancy from the list of legally qualified persons within five days after the list is received. If the list is not submitted to the Governor within the 15-day period, the Governor shall appoint, within five days thereafter, a legally qualified person of the same political party with which the person holding the office immediately preceding the vacancy was affiliated at the time of the previous election for that office: Provided, That any such person appointed by the Governor must have been affiliated with that political party for at least one year prior to the occurrence of the vacancy.

Furthermore,

1. (1) If the vacancy occurs on or before the primary cutoff date, then an election shall be held pursuant to §3-10-1 of this code; or

2. (2) If the vacancy occurs after the primary cutoff date, but on or before the general cutoff date, then the Governor shall issue a proclamation providing for:

   1. (A) A special filing period;
   2. (B) a special primary election to be held in conjunction with the upcoming general election; and (C) a special general election to be held not less than 84 nor more than 120 days following the date of the special primary election. Each election shall follow the requirements of §3-10-1 of this code that are not in conflict with this section.