It shall be the duty of the superintendent of each school district to make or cause to be made annual lists of the children enrolled in the schools of such district and who reside in such district, which lists shall be based upon the end of the first month enrollment required to be reported to the State Department of Education for the then current school year. The lists shall be made separately as to the townships in which such children reside. Such lists shall be filed with the superintendent of the custodial school district on or before December 31 of each year, and the lists shall be used in making the division of the available funds of each township during the ensuing calendar year, as provided by Section 29-3-119. The superintendent of the custodial school district shall make such lists available, upon request, to each school district sharing in the revenues of the township. Any school district failing to timely provide the list to the superintendent of the custodial school district shall forfeit its right to such funds unless the school board of the custodial school district and the school board of the other district or districts entitled to such funds have executed a written agreement providing for the distribution of such funds in a manner agreed upon by the school districts. All such lists shall be retained and preserved by the superintendent of the custodial school district as a public record. Such lists shall not be made, however, as to any township which is wholly within one (1) school district. If any superintendent of a school district participating in the division of such funds shall challenge in writing the accuracy of any such list, the Office of the State Auditor, upon receipt of such challenge, may, in its discretion, order and arrange for and supervise a recount of the children enrolled in the schools of such district and who reside in such district. All costs incurred in conducting the recount shall be borne by the challenging district and the district in which the recount is conducted on a pro rata basis, as determined from the results of the recount. Such costs may be paid from the school district’s share of the available township funds. Such recount, when obtained, shall supersede the original list for the purposes of Sections 29-3-115 through 29-3-123.