Whenever the officers of such district vote to terminate its corporate existence and whenever a petition signed by ten per cent of the total number of persons qualified to vote in the meeting of such district or twenty of the voters of such district, whichever is less, applying for a special meeting to vote on the termination of the district is received by the clerk, the clerk shall call a special meeting of the voters residing within such district, the notice of which shall be signed by the officers thereof, by advertising the same in the same manner as is provided in section 7-325. Not later than twenty-four hours before any such meeting, two hundred or more voters or ten per cent of the total number of voters, whichever is less, may petition the clerk of the district, in writing, that a referendum on the question of whether the district should be terminated be held in the manner provided in section 7-327. If, at such meeting, a two-thirds majority of the voters present vote to terminate the corporate existence of the district, or, if a referendum is held, two-thirds of the voters casting votes in such referendum vote to terminate the corporate existence of the district, the officers shall proceed to terminate the affairs of such district. The district shall pay all outstanding indebtedness and turn over the balance of the assets of such district to the town in which the district is located, if the legislative body of the town authorizes such action. No district shall be terminated under this section until all of its outstanding indebtedness is paid unless the legislative body of the town in which the district is located agrees in writing to assume such indebtedness. On completion of the duties of the officers of such district, the clerk shall cause a certificate of the vote of such meeting to be recorded in the land records of the town in which the district is located and the clerk shall notify the Secretary of the Office of Policy and Management.