Created a simple html demo page.
Attaching the file gave a 'disk full' error, so pasting the code here.
<!DOCTYPE html>
<html>
<head>
    <meta charset="UTF-8">
    <title>Tree - Combotree on same page Issue Demo</title>
    <link rel="stylesheet" type="text/css" href="themes/default/easyui.css">
    <link rel="stylesheet" type="text/css" href="themes/icon.css">
	<link rel="stylesheet" type="text/css" href="themes/color.css">
    <script type="text/javascript" src="jquery.min.js"></script>
    <script type="text/javascript" src="jquery.easyui.min.js"></script>
</head>
<body>
<h2>Tree + Combotree on same page Issue Demo </h2>
Having a Tree and a Combotree on the same page seems to cause malfunction of the combotree.
<br/>Try selecting something in the combotree. That fails ...
<br/>If you comment out the loadData for Tree, then the combotree works fine.
<br/> <br/>
<table width="50%">
  <tr>
    <td width="25%">
		Tree
		<hr/>
		<ul id="my_tree" class="easyui-tree"></ul>		
	</td>
	
    <td valign="top">
		Combotree
		<hr/>
		<input
			id="my_combo_tree"
			class="easyui-combotree"
			/>
	</td>
  </tr>
</table>
<script>
var hierarchichalData = [ {
    "id" : 50,
    "text" : "categ-1",
    "children" : [ {
      "id" : 52,
      "text" : "categ-1-1",
      "children" : null
    }, {
      "id" : 54,
      "text" : "categ-1-2",
      "children" : null
    } ]
  }, {
    "id" : 51,
    "text" : "categ-2",
    "children" : [ {
      "id" : 53,
      "text" : "categ-2-1",
      "children" : null
    } ]
  } ];
  
$(function(){
	// load the combo-tree
	$("#" + "my_combo_tree").combotree(
        'loadData', hierarchichalData
    );
	// load the tree
	// (combo-tree works fine if you comment out below loadData for the tree)
	$("#" + "my_tree").tree(
        'loadData', hierarchichalData
    );
});
	
</script>
</body>