Except as provided in paragraph (2) of this subsection, a candidate for public or party office who has been defeated based on the certified results of any election conducted under this article may petition for a recount of the votes cast for the office sought. A candidate may not petition for a recount if the margin of difference between the number of votes received by an apparent winner and the losing candidate with the highest number of votes for the office is greater than 5% of the total votes cast for those candidates. The petition shall specify that the recount be conducted: in all of the precincts in which the office was on the ballot; or only in the precincts designated in the petition. The petition shall be filed with the board with which the candidate’s certificate of candidacy was filed. The petition must be filed within 3 days after the results of the election have been certified. The State Board shall promptly notify each appropriate local board of a petition that is filed with the State Board. A local board shall promptly notify the State Board of a petition that is filed with the local board.