Any measure not returned by the governor to the house in which it originated shall be transmitted by the governor to the secretary of state. Any measure approved and signed by the governor shall be transmitted as soon as signed, and any measure not signed by him or her shall be transmitted upon the expiration of the sixth day, Sundays excepted, after the measure has been presented to him or her, if the general assembly is in session, or if the general assembly has adjourned, then upon the expiration of the tenth day after the adjournment.