In the following example, Click listeners throws an error. Wherein Double Click works. 

<ext:DropDownField ID="Field3" FieldLabel="Select Calendar"  runat="server" Editable="false" Width="300" Icon="SimpleArrowDown">
            <Component>
                <ext:TreePanel ID="TreePanel1"
                    runat="server" 
                    Header="false"
                    Icon="Accept"
                    Height="300"
                    Shadow="None"
                    UseArrows="true"
                    AutoScroll="true"
                    Animate="true"
                    EnableDD="true"
                    ContainerScroll="true" 
                    RootVisible="false">
                    <Root>
                        <ext:TreeNode>
                            <Nodes>
                                <ext:TreeNode Text="To Do" Icon="Folder">
                                    <Nodes>
                                        <ext:TreeNode Text="Go jogging" Leaf="true"  />
                                        <ext:TreeNode Text="Take a nap" Leaf="true"  />
                                        <ext:TreeNode Text="Clean house" Leaf="true"  />
                                    </Nodes>
                                </ext:TreeNode>
                                
                                <ext:TreeNode Text="Grocery List" Icon="Folder">
                                    <Nodes>
                                        <ext:TreeNode Text="Bananas" Leaf="true"  />
                                        <ext:TreeNode Text="Milk" Leaf="true"  />
                                        <ext:TreeNode Text="Cereal" Leaf="true"  />
                                        
                                        <ext:TreeNode Text="Energy foods" Icon="Folder">
                                            <Nodes>
                                                <ext:TreeNode Text="Coffee" Leaf="true"  />
                                                <ext:TreeNode Text="Red Bull" Leaf="true"  />
                                            </Nodes>
                                        </ext:TreeNode>
                                    </Nodes>
                                </ext:TreeNode>
                                
                                <ext:TreeNode Text="Kitchen Remodel" Icon="Folder">
                                    <Nodes>
                                        <ext:TreeNode Text="Finish the budget" Leaf="true"  />
                                        <ext:TreeNode Text="Call contractors" Leaf="true" />
                                        <ext:TreeNode Text="Choose design" Leaf="true"  />
                                    </Nodes>
                                </ext:TreeNode>
                            </Nodes>
                        </ext:TreeNode>
                    </Root>
                    
                    <Buttons>
                        <ext:Button ID="Button1" runat="server" Text="Close">
                            <Listeners>
                                <Click Handler="#{Field3}.collapse();" />
                            </Listeners>
                        </ext:Button>
                    </Buttons>
                    
                    <Listeners>
                        <DblClick Handler="#{Field3}.collapse();this.dropDownField.setValue(this.getSelectedNodes().text);" />
<%--                        <Click Handler="#{Field3}.collapse();this.dropDownField.setValue(this.getSelectedNodes().text);" />
--%>                    </Listeners>
                          
                 </ext:TreePanel>
            </Component>
            <Listeners>
                <Expand Handler="this.component.getRootNode().expand(true);" Single="true" Delay="10" />
            </Listeners>
        </ext:DropDownField>