It would be a start if you didn't have multiple checkboxes each named Checkbox1 or Checkbox2. They need to be uniquely named for the type of code event you are planning to work.
Then you will need to adjust your main code if you want the other checkbox pairs to work in a similar fashion.
Your checkbox entered is in the wrong Case selection group. It should be in the main group relating to CC
Code:
Case "Checkbox1"
If CC.Checked = True Then
ActiveDocument.SelectContentControlsByTitle("Checkbox2").Item(1).Checked = False
ActiveDocument.CustomDocumentProperties("Chk1").Value = 1
ActiveDocument.CustomDocumentProperties("Chk2").Value = 0
Else
ActiveDocument.SelectContentControlsByTitle("Checkbox2").Item(1).Checked = True
ActiveDocument.CustomDocumentProperties("Chk1").Value = 0
ActiveDocument.CustomDocumentProperties("Chk2").Value = 1
End If
ActiveDocument.Fields.Update
Case "Checkbox2"
If CC.Checked = True Then
ActiveDocument.SelectContentControlsByTitle("Checkbox1").Item(1).Checked = False
ActiveDocument.CustomDocumentProperties("Chk2").Value = 1
ActiveDocument.CustomDocumentProperties("Chk1").Value = 0
Else
ActiveDocument.SelectContentControlsByTitle("Checkbox1").Item(1).Checked = True
ActiveDocument.CustomDocumentProperties("Chk2").Value = 0
ActiveDocument.CustomDocumentProperties("Chk1").Value = 1
End If
ActiveDocument.Fields.Update
End Select
End Sub
You also have assorted controls without titles/tags. I would recommend that each control is uniquely titled. It makes things much easier when trying to program events.
You may find
Insert Content Control Add-In useful as a means of editing the controls (including the list box to remove the unwanted placeholder text).
Note that you don't need the module relating to Word 2007 compatibility. Word 2007 is not compatible with check box content controls, that were introduced with Word 2010.