RadDropDownTree has a built-in property that enables easy usage of the checkboxes. The default value of CheckBoxes property is None and there are three states that can be set to the nodes of the tree in the dropdown:
SingleCheck - Enables checking of nodes without effecting its child or parent nodes like in "CheckChildNodes" and "TriState".
CheckChildNodes - Checks all child and sub child nodes (if there are any) of a single node.
TriState - When set in the DropDownTree it allows for Nodes' CheckBoxes to have an additional, third state called Indeterminate. A Node's CheckBox is in Indeterminate state if it has both Checked and Unchecked CheckBoxes of child Nodes.
You can also use the ShowCheckAll properties that is available with the ButtonSettings as described in the ButtonSettings article.
From Q1 2014 RadDropDownTree has a built-in property called CheckNodeOnClick. Its default value is set to false but when it is set to true it allow checking the checkbox when clicking on the node itself. This functionality can be quite handy in mobile scenarios when touching the checkbox may be tricky for the users.