This neo-classical building, constructed to house the State Library and Supreme Court, is known as the "Old Finance Building." It has been renovated and expanded recently. Prior to renovation, in the 1990's the office of the Secretary of the Commonwealth occupied the lower floor of the building. It is still used for state offices and is adjacent to the Governor's Mansion on the eastern end of Capitol Square.
This is a circa 1893 view of the building as originally constructed (prior to the addition of a southern wing). The Governor's Mansion is visible to the left.
This is how the building appeared after an expansion circa 1901:
Current day view: