At any time following the formation of a district under this part and the issuance of the initial issue of bonds, any parcel of land may be added to the district if the owner of such parcel files with the legislative body a petition for such inclusion and the legislative body grants such petition. The legislative body shall not grant such petition until the petition has been approved by the parking place commission of the district and until a determination has been made by the legislative body and approved by the parking place commission as to the amount, if any, to be paid by such petitioner as an annexation fee and until the owner of such parcel has paid to the city such total fee, if any. The amount paid to the city shall be placed in the fund in which the proceeds of an ad valorem assessment would be placed. If such petition is granted, such parcel shall thereafter be entitled to the same rights as those which apply to other lands in the district and shall be subject to all ad valorem assessments thereafter levied in the district under this part.