How to implement itemChecked and itemUnchecked signals for QTreeWidget in PyQt4?

To avoid problems with recursion when using the itemChanged signal, try temporarily blocking signals until the handler has completed:

def handle(self, item, column):
    self.treeWidget.blockSignals(True)
    if item.checkState(column) == QtCore.Qt.Checked:
        self.handleChecked(item, column)
    elif item.checkState(column) == QtCore.Qt.Unchecked:
        self.handleUnchecked(item, column)
    self.treeWidget.blockSignals(False)

UPDATE

The other part of your question asked about emitting a signal only when an item is checked.

One way to do this would be to subclass QTreeWidgetItem and reimplement it's setData function:

class TreeWidgetItem(QtGui.QTreeWidgetItem):
    def setData(self, column, role, value):
        state = self.checkState(column)
        QtGui.QTreeWidgetItem.setData(self, column, role, value)
        if (role == QtCore.Qt.CheckStateRole and
            state != self.checkState(column)):
            treewidget = self.treeWidget()
            if treewidget is not None:
                treewidget.itemChecked.emit(self, column)

class Window(QtGui.QTreeWidget):
    itemChecked = QtCore.pyqtSignal(object, int)

    def __init__(self, rows, columns):
        QtGui.QTreeWidget.__init__(self)
        self.itemChecked.connect(self.handleItemChecked)

    def handleItemChecked(self, item, column):
        print 'ItemChecked', int(item.checkState(column))