(A) There are three classes of municipal corporations:
(1) First Class, with a population of 5,000 or over;
(2) Second Class, with a population between 500 and 5,000;
(3) Third Class, with a population of less than 500.
(SDCL § 9-2-1)
(B) The municipality may change its classification if the territory of the municipality has changed substantially since the last preceding census. The governing body by resolution may authorize and direct its auditor or clerk to determine the population by filing in his or her office a certificate showing the whole number of persons who voted at the last preceding annual municipal election, which number multiplied by three shall constitute the population for the purpose of classification until the next federal census shall have been completed.
(SDCL § 9-2-2)