The Departments of Finance of New Castle County and of Sussex County shall, during the months of January and July in each year, audit, inspect, and examine the books, accounts, papers, records, and dockets of the several county officers and ascertain the amounts due to the county in fees. During those months, the Departments of Finance of New Castle County and of Sussex County shall report in writing to their respective county governments, which shall cause the same to be entered at large upon their minutes and published for public distribution.