Java Code:
import org.eclipse.swt.SWT;
import org.eclipse.swt.graphics.Point;
import org.eclipse.swt.widgets.Display;
import org.eclipse.swt.widgets.Event;
import org.eclipse.swt.widgets.Listener;
import org.eclipse.swt.widgets.Shell;
import org.eclipse.swt.widgets.Tree;
import org.eclipse.swt.widgets.TreeItem;

public class DetectMouseDownInTreeItem {

  public static void main(String[] args) {
    Display display = new Display();
    Shell shell = new Shell(display);
    final Tree tree = new Tree(shell, SWT.BORDER | SWT.MULTI);
    for (int i = 0; i < 12; i++) {
      TreeItem treeItem = new TreeItem(tree, SWT.NONE);
      treeItem.setText("Item " + i);
    }
    tree.addListener(SWT.MouseDown, new Listener() {
      public void handleEvent(Event event) {
        Point point = new Point(event.x, event.y);
        TreeItem item = tree.getItem(point);
        if (item != null) {
          System.out.println("Mouse down: " + item);
        }
      }
    });
    tree.setSize(200, 200);
    shell.setSize(300, 300);
    shell.open();
    while (!shell.isDisposed()) {
      if (!display.readAndDispatch())
        display.sleep();
    }
    display.dispose();
  }

}