(1) The township board may proceed to carry out an improvement as provided in this act unless written objections to the improvement are filed with the township board at or before the hearing provided in section 4 by property owners as follows:
    (a) For an improvement under section 2(1)(a), (b), (d), (e), (f), (h), (i), (j), (l), (n), or (o) by the record owners of land constituting more than 20% of the total land area in the proposed special assessment district.

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    (b) For an improvement under section 2(1)(c), (g), (k), or (m), by the record owners of land constituting more than 20% of the total frontage upon the road, bicycle path, or sidewalk.
    (2) A township board may require the filing of a petition meeting the requirements of subsection (3) before proceeding with an improvement under this act.
    (3) If written objections are filed as provided in subsection (1), or if the township board requires a petition before proceeding, the township board shall not proceed with the improvement until there is filed with the board a petition signed as follows:
    (a) For an improvement under section 2(1)(a), (b), (d), (e), (f), (h), (i), (j), (l), (n), or (o) by the record owners of land constituting more than 50% of the total land area in the special assessment district as finally established by the township board.
    (b) For an improvement under section 2(1)(c), (g), (k), or (m), by the record owners of land constituting more than 50% of the total frontage upon the road, bicycle path, or sidewalk.
    (4) Record owners shall be determined by the records in the register of deeds’ office as of the day of the filing of a petition, or if written objections are filed as provided in subsection (1), then on the day of the hearing. In determining the sufficiency of the petition, lands not subject to special assessment and lands within a public highway or alley shall not be included in computing frontage or an assessment district area. A filed petition may be supplemented as to signatures by the filing of an additional signed copy or copies of the petition. The validity of the signatures on a supplemental petition shall be determined by the records as of the day of filing the supplemental petition.