When considered necessary, an audit shall be made of the state treasury and the custodial funds of the treasurer of state, including the office of the commissioners of the sinking fund, by a committee of the general assembly or of either house thereof authorized by resolution, or by a committee of persons not members of the general assembly appointed by resolution of the general assembly. When required by law, or if in the opinion of the governor the public interest requires it, the governor shall appoint a public accountant who, together with the secretary of state, without previous notice or information from them of the intended audit, shall immediately make an audit of all his records concerning, and the assets of, the state treasury and the custodial funds of the treasurer of state.