Upon hearing of any protests made by the owners of property within the improvement district in the time and in the manner provided by law, if the governing body shall determine the protests to be insufficient, it may proceed with the improvement as in the case of other special improvements; provided, that before so proceeding a certified transcript of the resolution of necessity must be recorded in the office of the recorder, and any person aggrieved thereby may appeal to the district court of the county in accordance with the procedure provided in section 28-34-01, but only on the ground that the establishment of the mall or construction of the skyway in accordance with the resolution will unreasonably and arbitrarily obstruct the public use of and interest in the designated street or streets, or that such resolution has been adopted in a manner contrary to law. Notwithstanding the establishment of a mall or skyway, or the improvement of any street or any portion thereof as a part of such mall or skyway, or any limitation of the use thereof by vehicles, the city and the governing body shall retain at all times their police powers and other powers and rights pertaining thereto, and no such action shall constitute a vacation, in whole or in part, of any portion of a city street.