§ 2. Public buildings. Except where otherwise prescribed by law, the commissioner of general services shall have supervision and control of public buildings of the state of New York, including the capitol and executive mansion, with the buildings, grounds and premises adjacent or appurtenant thereto or connected thereto or connected therewith belonging to the state, so far as such grounds and premises now or hereafter shall be laid out and completed, and the entire public sidewalks bordering upon the capitol grounds and parks for the purpose of keeping such sidewalks at all times clear of snow, ice, dirt and all other obstructions.