Any claim for damages arising against the state under Section 4114 or 4115 shall be presented to the Department of General Services in accordance with Part 3 (commencing with Section 900) and Part 4 (commencing with Section 940) of Division 3.6 of Title 1 of the Government Code and, if not covered by insurance, shall be payable only out of funds appropriated by the Legislature for that purpose. If the state has elected to acquire liability insurance, the Department of General Services may automatically deny this claim.