On or before the first Monday in September in each year the supervisors of each diking, drainage or sewerage improvement district shall make and file with the board of the county containing such district, a statement and estimate in writing of the amount required for the maintenance of the system of improvements of said district for the ensuing fiscal year. The board shall, on or before the first Monday in October next ensuing, levy assessments for the amount of said estimate, or such amount as it shall deem advisable, upon the property within the district and against the state, the county containing such district, and the cities, towns and other municipal corporations within such district in respect of all highways, roads and streets and other lands, improvements, and facilities chargeable therewith owned by them respectively within such district. Said assessments shall be levied in the same proportion as the assessments to pay the original cost of construction of said system of improvements: PROVIDED HOWEVER, That when a determination or redetermination of benefits accruing to the properties within the district from the maintenance of the district's system of improvements or from the maintenance of the district's diking system and drainage system separately shall have been made, as hereinafter in this chapter provided, then the assessments for maintenance shall be levied in proportion to the benefits accruing to each piece or parcel of property and improvements benefited according to the latest determination of such benefits. Each such levy as made shall be certified by the auditor to the treasurer, who shall extend the same upon the district assessment roll.