The best way to implement your desired scenario would be to use data binding to your view-model. This of course would be appropriate if you are using data-bound TreeView.
If we assume you are using a data-bound TreeView, the steps would be like follows:
1) Place a check box inside your TreeViewItems data template.
2) Create an IsChecked property in your view-model objects.
3) Use a style binding with two way mode between IsChecked property of the data template check box and IsChecked property in your view model.
4) In the view model IsChecked property setter make a call to function that unchecks all other items and leave the current one checked.
This way you could encapsulate your business logic inside your view model and test it easily eliminating the concerns related to RadTreeView.
However, if RadTreeView is xaml defined and you are not using data binding probably you should use code behind.
Hope this helps. Please let us know if you need more info.
the Telerik team