After the department has made and recorded a determination that there is need, in the interest of the public health, safety and welfare, for the organization of a district in a particular territory and has defined the boundaries thereof, it shall, within a reasonable time after entry of the finding that there is need for the organization of the proposed district and the determination of the boundaries thereof hold a referendum within the proposed district upon the proposition of the creation of the district and cause due notice of such referendum to be given. The question shall be submitted by ballots upon which the words "For creation of a soil and water conservation district of the lands below described and lying in the county(ies) of (and )" and "Against creation of a soil and water conservation district of the lands below described and lying in the county(ies) of (and )" shall appear with a square before each proposition and a direction to insert an X mark in the square before one or the other of said propositions as the voter may favor or oppose creation of such district. The ballot shall set forth the boundaries of such proposed district as determined by the department. All owners of lands lying within the boundaries of the territory, as determined by the department, shall be eligible to vote in such referendum. Only such landowners shall be eligible to vote.