This is the Department of Libraries/Supreme Court building at 111 State Street in Montpelier (immediately to the right of the Capitol), which houses the Department of Libraries' Reference & Law Services Unit, containing the law library.  You can enter the front door and be directed to the library, but the "official" front door is in the side (the Gov. Davis Ave side) of the Pavilion Office Building, to the right at 109 State Street (the porches are visible in photo on right).