When the candidate of a political party, after having been nominated to the office of state senator or representative, shall die, be certified by a state convention for a statewide office, withdraw from the district, become physically unfit, or become disqualified for any reason, the members residing within said senatorial or representative district of the county executive committees of such candidate’s political party for the counties comprising said senatorial or representative district shall meet at a time and place designated by the chairperson of the state central committee of such political party and notice of such meeting shall be sent to all such members of the county executive committees. The meeting shall be conducted by the secretary of the state central committee or his or her duly authorized agent, but said secretary or agent shall not be privileged to vote at such meeting. A candidate to fill the vacancy shall be selected by a majority vote of the committee members present and voting: Provided, That if such vacancy occurs in a senatorial or representative district wholly within 1 county, a candidate to fill the vacancy shall be selected by the county executive committee of the county by a majority vote thereof. The name of the candidate so selected shall be certified immediately by the chairperson and the secretary of said committee to the secretary of state in those districts comprising 2 or more counties and to the county clerk in those districts contained within 1 county. The certification shall be sent in any case to the board of election commissioners for each county, whose duty it is to prepare the official ballots; and said board shall cause to be printed or placed upon such ballots, in the proper place, the name of the candidate so selected and certified to fill such vacancy.