The lifeguard chair sits empty at a busy Silver Sands State Park beach in Milford, Conn. on Tuesday, June 19, 2018.Brian A. Pounds / Hearst Connecticut Media With sunny skies and temperatures in the 80s, many people are heading to shoreline state parks,. Too many. By 1 p.m., the state Department of Energy and Environmental Protection announced that four Long Island Sound state park beaches are closed to new visitors because parking lots are full. The state parks closed include Sherwood Island in Westport, Silver Sands in Milford, Hammonasset in Madison and Rocky Neck in East Lyme. DEEP has limited parking at state parks because of social distancing requirements during the cornonavius pandemic. It has also banned swimming at inland parks. For the last updates on state park closings today, click here.