Neb. Rev. Stat. §§ 16-254
Any city of the first class may by ordinance provide for regulation of traffic, public use and conduct of invitees upon specified parking lots, shopping centers and similar semipublic but privately owned places located within the city limits of such city when the owners or operators of such semipublic places make written request for the same. Such ordinances may provide for regulation of the flow of traffic, speed limits, offenses against the public morals, unlawful assembly, trespass and similar offenses to the same effect and with the same authority as can be done in public thoroughfares, public parking lots and other public places. Such ordinance shall provide penalties within the limits of authority granted to cities of the first class for violation of city ordinances. Nothing in this section shall require the city to furnish labor, material, supervision, personnel or services in connection with the establishment, supervision or enforcement of such ordinance or the maintenance or upkeep of such parking areas.
Neb. Rev. Stat. §§ 16-254