In the event a petition is presented to the legislative body of the municipality averring the willingness of each of the signers to pay their pro rata share of the entire cost of any improvement such as is authorized by this chapter, and relieve the municipality from the payment of any part of the improvement as to any street, highway, or alley, or part or parts thereof, which petition is signed by the owners of at least seventy-five percent (75%) of the frontage of the lots or parcel of land abutting on such street, highway, or alley or part or parts thereof, proposed to be thus improved, such petition may be granted by the legislative body; and then proceedings may be had under this chapter and chapter 33 of this title, the same in all respects as if the improvement had been begun by the legislative body on its own initiative. Bonds may be issued and assessments shall be made, except that the assessments shall, in such event, be made for the entire cost of the improvement, and bonds may be issued for the entire cost instead of assessments being made and bonds being issued for only two thirds (2/3) of the cost of the improvements; provided, that no assessment under this section shall in any event exceed on any lot one half (½) of the assessed value of the lot for municipal taxes for the current year, and all other provisions of this chapter and chapter 33 of this title shall be applicable in respect of any improvement made under this section, except as in this section otherwise expressly provided.