(1) When the assessment is completed, the commissioners shall subscribe the assessment and deposit it with the clerk at the circuit court where the district was organized. The book shall be kept and preserved as a public record, and a list of the lands and assessments in the county shall be filed with the respective circuit clerk and recorder in each of the counties.
(2) Upon the filing of the assessment, the circuit clerk shall give notice of the fact by publication two (2) weeks in some newspaper in each of the counties in which the lands of the district may be situated. The notice shall give a description of the lands assessed for the proposed improvement. The owners of the lands, if they desire, may appear before the circuit court on a day therein named and fixed by the clerk and present complaints, if they have any, against the assessment of any lands in the district.