Such institution shall prepare a written itemized statement of its claim, in such form and detail as the controller of the county shall prescribe, which statement shall be signed and sworn to by its president, attested by its secretary, and shall be under its corporate seal, if incorporated; or, if not incorporated, the written statement shall show the fact, and shall be signed and sworn to by its superintendent, and attested by its chief clerk; and, when so prepared and presented to the proper officers of the respective county, it shall be audited, and the sum or sums found to be reasonably and equitably due by such officers shall be paid.