A counterpetition to a question filed under § 12-103 of this subtitle may be filed by a voter eligible to vote for that question, if: the petition filed under § 12-103 of this subtitle did not specify all of the precincts in which the question was on the ballot; and on completion of the recount, the outcome of the election is changed. A counterpetition shall be a request for a recount of the votes for the question in the precincts not specified by the petitioner under § 12-103 of this subtitle. If the question was on the ballot in one county, the counterpetition shall be filed in that county. If the question was on the ballot in more than one county, the counterpetition shall be filed with the State Board. The petition shall be filed within 2 days of the determination under subsection (a)(2) of this section. The State Board shall promptly notify each appropriate local board of a counterpetition that is filed with the State Board. A local board shall promptly notify the State Board of a counterpetition that is filed with the local board.