In case the boundary line of a district crosses the boundary line of a county election precinct only those voters within the district and within the precinct who are registered as being voters within the district shall be permitted to vote, and for that purpose the county elections official may provide two sets of ballots within those precincts, one containing the names of candidates for office in the district, and the other not containing those names, and it shall be the duty of the election officers in those precincts to furnish only those persons registered as voters within the district with the ballots upon which are printed the names of the candidates for office in the district.