Neb. Rev. Stat. §§ 23-341
Two-thirds of the cost of any such improvement authorized by sections 23-339 and 23-340 outside the corporate limits of such city and not adjacent thereto, as mentioned in section 23-339, shall be paid by said county board out of the road funds of the county, and one-third by special assessment of all real estate abutting on or adjacent to such improvement to a depth not exceeding five hundred feet on each side thereof, in proportion to the special benefits to such real estate by reason of such improvements. The benefits to such real estate shall be determined by the board, after publication in a newspaper of general circulation in the county, of notice to the owners of said real estate at least ten days prior to such determination. Such assessment may be made according to the foot frontage of real estate along the line of such improvement or according to such other rule or method as the board may adopt for the distribution and equalization of said one-third of the cost. The amount so assessed shall be placed upon the tax list for the ensuing year and collected in the same manner at the same time as the taxes of other property, and, when collected, shall be held in a special fund and used only in the payment of the cost of that particular improvement, as specified herein.
Neb. Rev. Stat. §§ 23-341