A school district board may not proceed to obtain approval as a participating district in an area career and technology center if a petition for referendum of the question of said school district participating in an area career and technology center signed by twenty percent of the qualified electors of said school district voting at the last annual school election is filed with the school board within sixty days of the publication of the resolution provided for in section 15-20.2-12. When such petition is filed, the school board may not obtain approval as a participating district in an area career and technology center until the question of whether the district shall enter into an area career and technology center has been submitted to the qualified electors of the district. If a majority of the total number of votes cast on the question within the school district is in favor of the question, the school board may proceed to obtain approval as a participating district in an area career and technology center.