It is the duty of the county clerk to examine and compare the assessment rolls of the county with the inventories or reports of administrators and executors as soon as filed with the county clerk, for the purpose of ascertaining whether any personal property of any estate is subject under this chapter to back assessment or reassessment. In case such examination shows any personalty subject to such back assessment or reassessment, the clerk shall so report to the county trustee, who shall back assess or reassess the personalty under this part, and add the penalty previously designated.