1. When a district is contained wholly within a city, the board may convey to such city, at the discretion of the district and with the consent of the governing body of the city, all of the property of the district upon the condition that such city:
(a) Will operate and maintain such property; and
(b) Assumes all of the indebtedness of such district upon such conditions as the governing body of the city and the board of the district may agree.
2. Upon such conveyance and assumption of indebtedness, the district shall be dissolved and a certificate to such effect shall be signed by the clerical officer of the city and filed with the Secretary of State and clerk of the county or city in which the ordinance creating the district was filed.