The clerk of any town, the mayor of any city or the warden of any borough in which a vacancy occurs in any elective office shall notify the Secretary of the State of such vacancy within five days thereafter; and, in the case of a vacancy in the office of town clerk, the first selectman of such town or, in the case of a vacancy in the office of mayor of a city or of warden of a borough, the clerk of such city or the clerk of such borough, as the case may be, shall so notify the Secretary of the State of such vacancy. The officer required to give such notice shall, within five days after any such vacancy has been filled, notify the Secretary of the State of the name and address of the person chosen to fill the vacancy, the time and method of its filling and the law under which it was filled.