In order to provide additional means for carrying on an animal damage control program for the management and control of coyotes, bobcats, foxes, and other predatory animals destructive of sheep and cattle, county boards may levy in any year a tax of not to exceed twenty cents per head on sheep and cattle on the following conditions:

(1) That a petition to the county board requesting such levy, signed by sixty-seven percent of the owners of the sheep, the cattle, or the sheep and cattle in the county as of January 1 of each year, be filed with the board on or before July 1; and

(2) That a planned program for the management and control of such predatory animals be approved by the county board each year in which such levy is to be made. Such planned program may include entry in the animal damage control program authorized by section 23-358 or any other program approved by the board and designed to manage and control such predatory animals. The proceeds of such levy shall be placed in a separate fund and shall be applied exclusively to carrying out the program adopted. For each year in which such a levy is deemed necessary, a petition shall be presented to the county board for approval as provided in this section.