Select elements are notoriously tricky in Internet Explorer. I don't think there is any way of reliably determining if one is open or closed.

I can see if the select is open, and then when it closes if the user selects a new option, or completely blurs the select. However, if you click on the same option, or just click out of the select once (closing it but not blurring it), it still shows "down". Working on a more complete solution. So, expect this answer to have edits...

<script type="text/javascript" src="http://code.jquery.com/jquery-latest.pack.js"></script>
<script type="text/javascript">
  var selected
$( document ).ready(


 function()
 { 
  $( '#test' )
      .mousedown( function(){ console.log( 'down' ); selected = $( this ).val() } )
      .blur( function(){ console.log( 'out' ) } )
      .change( function(){ console.log( 'out' ) } )
      .mouseleave( function(){ console.log( 'out' ) } )
      .mouseup( function(){ 
         if( $( this ).val() == selected ) 
           console.log( 'out' )
    }
   )
 } // function

) // ready
</script>

<select id="test">
 <option>1</option>
 <option>2</option>
</select>

Edit: added mouseout

Edit2: added mouseup - works now!

A more complete solution would be:

<script type="text/javascript" src="http://code.jquery.com/jquery-latest.pack.js"></script>
<script type="text/javascript">
var selected,selected2
$( document ).ready(


 function()
 { 
  $( 'select[id$="test"]' )
      .mousedown( function(){ 
        console.log( 'predown' );
        if( $( this ).val() != selected ) {
          console.log( 'down' ); 
          selected = $( this ).val();
          selected2=null;} 
        else  
          selected=null;} )
      .blur( function(){ if (selected2==selected) {
        console.log( 'outb' );
        selected=null;
        selected2=null;} } )
      .mouseup( function(){ console.log( 'preoutu' );
         if( $( this ).val() != selected || $( this ).val() == selected2 ) {
            console.log( 'outu' );
            selected=null;
            selected2=null;
         }
         else
           selected2=$( this ).val();   
    }
   )
 } // function

) // ready
</script>


<select id="1test">
 <option>1</option>
 <option>2</option>
</select>
<select id="2test">
 <option>1</option>
 <option>2</option>
</select>