K.S.A. 12-1809

The cost of all sidewalks shall be assessed against the property abutting on the sidewalk: Provided, That where a sidewalk is condemned and a new sidewalk constructed, the materials of the old sidewalk shall be the property of the city, except in those cases where the property owner builds the new sidewalk and pays for the same without any assessment having to be made, and in such cases he or she shall remove the old material from the street.