In counties in which districts are located the county elections official is hereby given authority, and is authorized to have printed upon the official ballots provided for voters at elections for directors a heading in the same form as that provided by the Elections Code for nonpartisan officers, which heading shall be marked “Water Replenishment District,” with a subheading “For a Member of the Board of Directors, Division ____ (here inserting the number of the division)—Vote for One,” and beneath which shall appear the names of the candidates for the office of member of the board for the division of the district, with the appropriate blank space for the writing in of the name of a candidate if desired by the voters, and with a voting square placed opposite the space. The ballots thus provided shall be furnished by the precinct officers only to those voters within their respective precincts who shall appear on the register as duly registered voters within that division of the district, and in precincts that lie partly within that district and partly without the precinct board shall be supplied with two kinds of ballots by the county elections official, one of which shall contain the matters hereinabove set forth for the use of voters of the district, and the other of which shall be without the heading containing the names of candidates for the office of member of the board, and which shall be furnished to those voters who are not voters of the district and who are voters of the precinct.