State employees started relocating just after Thanksgiving, and by the end of January, the building will become the workplace for about 700. The renovated space will primarily be the domain of the state’s constitutional officers, including the attorney general, comptroller, treasurer and secretary of the state. The structure also will house the state auditors and later this year, the teachers’ retirement board. The state faces a deadline of March 31 to move all personnel and equipment out of 55 Elm St. or be hit with a higher month-to-month lease. The State Office Building renovation is part of a larger plan to consolidate state workers into buildings the state owns to save on leasing costs. The makeover of the State Office Building was controversial for its $205 million price tag, including a $34 million, 1,007-space parking garage on nearby Buckingham Street.