Neb. Rev. Stat. § 16-651

Whenever the owners of lots and lands abutting upon any street or alley, or part thereof, within a city of the first class, representing two-thirds of the feet front abutting upon such part of street or alley desired to be graded, shall petition the city council to grade such street or alley, or part thereof, without cost to the city, the mayor and city council shall order the grading done and assess the costs thereof against the property abutting upon such street or alley or such part thereof so graded. For this purpose the mayor and city council shall create suitable grading districts, which shall be consecutively numbered.