(1) A city, village, or township may contract with the secretary of state or the United States bureau of the census to have conducted a special census of its population. The entire cost of the census shall be borne by the city, village, or township. The special census shall provide for separate identification by institution of wards, patients, or convicts in tax supported institutions in accordance with definitions used by the United States bureau of the census in the enumeration of the preceding statewide federal census. The results of the special census shall be certified to the department of management and budget by the secretary of state.

    (2) The results of the special census as certified in subsection (1) shall be utilized for the purpose of making distributions under section 14a starting on the July 1 next following the date of certification of the results. Only 1 special census may be utilized between 2 statewide federal censuses. The enumeration date of a special census utilized under this act shall not be less than 3 years from the enumeration date of a regular statewide federal decennial census.

    (3) A city, village, or township that on the enumeration date of a special census is determined to have an increase of population of 10% or more over its population as determined by the last preceding statewide federal census shall receive its share of revenues distributed under section 14a based on its population increase which exceeds the estimated state growth rate. Estimated state growth rate means the estimate determined by the department of management and budget as of the enumeration date of a special census.