Section 11. The probate court in each county shall require every public administrator in such county to render an account of his proceedings under any letters of administration at least once a year until the trust is fulfilled. When, on final settlement of an estate, it appears that money remains in the hands of such administrator which by law should have been deposited with the state treasurer, the court shall certify that fact and a statement of the amount so withheld to said treasurer, who, unless such deposit is made within one month after the receipt of such notice, shall cause the bond of the administrator to be prosecuted for the recovery of such money.