After the local agency formation commission approves the formation of the district, notwithstanding Section 13823, if the board of supervisors finds that the petition filed with the executive officer of the local agency formation commission pursuant to Section 13819 has been signed by not less than 51 percent of the registered voters residing within the territory to be included within the proposed district, the board of supervisors may dispense with an election and adopt the resolution required pursuant to Section 13829. The initial members of the board of directors of the district shall be determined pursuant to Article 3 (commencing with Section 13834) of Chapter 3 of Part 3 of Division 12.