Upon the passage of any such ordinance, it shall be the duty of the officer specified therein to file a petition in the circuit court in said county, or, if such city, village or town is situated in more than one county and the proposed improvement lies in more than one county, then in the circuit court in the county in which the major part of the territory to be affected thereby is situated, in the name of such municipality, praying that steps be taken to levy a special assessment for the said improvement in accordance with the provision of the said ordinance. The several circuit courts of this State shall have jurisdiction of any proceedings under this Act. There shall be attached to or filed with such petition, a copy of the said ordinance, certified by the clerk under the corporate seal.
     Upon the filing of such petition, the superintendent of special assessments, in cities where such officer is provided for by law, otherwise some competent person appointed by the Mayor and City Council of Cities and the President and Board of Trustees of villages and incorporated towns, shall make a true and impartial assessment of the cost of the said improvement upon the petitioning municipality and the property benefited by such improvement.