If the territory of such school district as is provided for in section 37-59-19, lies in two or more counties, bonds may be issued as provided herein by the board of supervisors of the county having the greatest assessed valuation of taxable property within such district, upon petition of a majority of the qualified electors residing within the district as a whole. In such cases, a counterpart of the petition shall be separately circulated in that part of the district situated within each of the counties involved, and the said petitions shall be filed with the respective boards of supervisors. Each such board shall thereupon determine, by resolution entered upon its minutes, the number of qualified electors of such county residing within such district, and the number of qualified electors of such district who have signed such petition, and shall transmit a certified copy of such resolution and of such petition to the board of supervisors of the county having the greater assessed valuation of taxable property within such district. The latter board shall thereupon determine, by resolution entered upon its minutes, the total number of qualified electors residing within such district as a whole, and the total number of qualified electors of such district who have signed such petitions. If the latter board thereupon finds and determines that such petitions have been signed by a majority of all of the qualified electors residing within such district, regardless of county lines, such board may proceed to issue bonds in the amount and for the purpose or purposes set forth in such petition.

The maximum amount of such bonds which may be issued by petition shall not exceed the sum of ten thousand dollars ($10,000.00), and the total amount of bonds so issued by petition in any twelve-month period shall not exceed the sum of ten thousand dollars ($10,000.00).