When any person applies to the county treasurer to pay the diking, drainage or sewerage improvement district assessments upon a portion of a lot, tract or parcel upon which special benefits have been confirmed, the county treasurer shall refer such matter to the county engineer for investigation. The county engineer shall apportion the total benefits found as to such lot, tract or parcel between the portions thereof in such manner as may be fair, just and equitable taking into account all factors, situations and conditions which may be lawfully taken into consideration in determining such special benefits. Unless the several owners interested in said lot, tract or parcel assent to the apportionment so made, the county engineer shall give notice to the apportionment by mail to them, if known. Upon assent of the interested owners or after the expiration of five days from the date of notice without the filing of a written protest to the apportionment, the county engineer shall certify in writing the apportioned benefit valuations to the county treasurer. The county treasurer, upon receipt of such certification, shall accept payment and issue receipt on the certified apportionment. If a written protest to such apportionment is filed with the county treasurer, the matter shall be heard by the county commissioners at their next regular session for final apportionment and the county treasurer shall accept and receipt for such assessments as determined and ordered by the county commissioners.