Any county, subject to the provisions of the Constitution of the state of Missouri, may establish, maintain, manage and operate a public health center in the following manner: whenever the county commission shall be presented with a petition signed by at least ten percent or more of the voters of the county, as determined by the number of votes cast for governor at the preceding general election, asking that an annual tax not in excess of forty cents on each one hundred dollars of the assessed valuation of property in the county, be levied for the establishment, maintenance, management and operation of a county health center and the maintenance of the personnel required for operation of the health center, or by majority vote of the county commission in any county of the first classification with more than eighty-two thousand but fewer than eighty-two thousand one hundred inhabitants, or by majority vote of the county commission in any county of the third classification without a township form of government and with more than sixteen thousand six hundred but fewer than sixteen thousand seven hundred inhabitants, the county commission shall submit the question to the voters of the county at an election.