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How to check an overlay type after clicking
  1. After you create a Marker or Geometry that you want then let's use event 'overlayClick' 
    map.Event.bind('overlayClick', function(overlay) {
  if (overlay instanceof longdo.Marker) {
    document.getElementById('overlayselect').innerHTML = 'Marker';
  } else if(overlay instanceof longdo.Polyline){
    document.getElementById('overlayselect').innerHTML = 'Polyline';
  } else if(overlay instanceof longdo.Polygon){
    document.getElementById('overlayselect').innerHTML = 'Polygon';
  } else if(overlay instanceof longdo.Dot){
    document.getElementById('overlayselect').innerHTML = 'Dot';
  } else if(overlay instanceof longdo.Circle){
    document.getElementById('overlayselect').innerHTML = 'Circle';
  }
});
    • overlayClick: User click overlay event
    Example
    2. click overlay

    More information: Event Handler