The bank shall continue to be subject to the supervision and examinations required by the laws of this state, except that the federal reserve board shall have the right, if it deems necessary, to make examinations, and the authorities of this state having supervision over the bank or trust company may disclose to the federal reserve board, or to examiners duly appointed by it, all information in reference to the affairs of any bank that has become, or desires to become, a member of a federal reserve bank.