(1) When a special election is called to fill any state district office or legislative office and where only one (1) person has duly qualified with the State Board of Election Commissioners to be a candidate in the special election within the time prescribed by law for qualifying as a candidate, the State Board of Election Commissioners shall make a finding and determination of that fact, which shall be duly entered upon its official minutes.
(2) A finding and determination and certification to office by the State Board of Election Commissioners, as herein provided, shall dispense with the holding of the special election.
(3) A certified copy of the finding and determination of the State Board of Election Commissioners shall be filed with the Governor, and the Governor shall appoint the candidate so certified to fill the unexpired term.