Whenever an affirmative vote of a majority of the eligible employees in any coverage group is required as a condition of an application under this article, such requirement shall be deemed satisfied by the signatures of a majority of such eligible employees on a written petition to the legislative or governing body requesting such application. For the purposes of such requirement an employee shall be an eligible employee in each coverage group of a public agency in which he is employed and which is included in a separate application of the public agency.