If the assessment district includes property out of the territorial jurisdiction of the city conducting the proceeding, the legislative body of the city having jurisdiction thereover may in its discretion order by resolution, a copy of which shall be transmitted to the legislative body conducting the proceeding, that any part of the cost or expenses of the work shall be paid out of the treasury of the city. A liability for the portion of the cost set forth in the resolution shall thereby be created against the city ordering such contribution.