Notwithstanding that any school district or county may have exercised the privilege accorded under § 59-31-410 not to come under the provisions of this article, any such school district or county may retract any such election by filing with the State Board of Education a written statement, which for any school district shall be signed by the board of trustees of such district and approved by the Senator and at least one half of the representatives from such county and for any county shall be signed by the county board of education and approved by the Senator and at least one half of the representatives of such county, in either case to the effect that the district or the county, as the case may be, desires to retract any such election theretofore made by it and to come under the provisions of this article. Upon any such statement being filed, any such school district or county, as the case may be, shall thereupon come under the provisions of this article.