1. When a district abuts a city or town, the board shall have the power to convey to such city or town, at the discretion of the district and with the consent of the governing authority thereof, all of the property of such district upon the condition that such city or town:
(a) Will operate and maintain such property, regardless of whether the area comprising the district is annexed to the municipality; and
(b) May assume all of the indebtedness of such district upon such conditions as the county or town and the governing body 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 or town and filed with the Secretary of State and county clerk of any county in which the ordinance creating the district is filed.