Index: Doc/library/os.path.rst
===================================================================
--- Doc/library/os.path.rst	(revision 82145)
+++ Doc/library/os.path.rst	(working copy)
@@ -201,6 +201,7 @@
    Normalize the case of a pathname.  On Unix and Mac OS X, this returns the
    path unchanged; on case-insensitive filesystems, it converts the path to
    lowercase.  On Windows, it also converts forward slashes to backward slashes.
+   Raise a TypeError if the type of the path is not ``str`` or ``bytes``.
 
 
 .. function:: normpath(path)
Index: Lib/os2emxpath.py
===================================================================
--- Lib/os2emxpath.py	(revision 82145)
+++ Lib/os2emxpath.py	(working copy)
@@ -36,6 +36,9 @@
     """Normalize case of pathname.
 
     Makes all characters lowercase and all altseps into seps."""
+    if not isinstance(s, (bytes, str)):
+        raise TypeError("normcase() argument must be str or bytes, "
+                        "not '{}'".format(s.__class__.__name__))
     return s.replace('\\', '/').lower()
 
 
Index: Lib/posixpath.py
===================================================================
--- Lib/posixpath.py	(revision 82145)
+++ Lib/posixpath.py	(working copy)
@@ -49,6 +49,9 @@
 def normcase(s):
     """Normalize case of pathname.  Has no effect under Posix"""
     # TODO: on Mac OS X, this should really return s.lower().
+    if not isinstance(s, (bytes, str)):
+        raise TypeError("normcase() argument must be str or bytes, "
+                        "not '{}'".format(s.__class__.__name__))
     return s
 
 
Index: Lib/ntpath.py
===================================================================
--- Lib/ntpath.py	(revision 82145)
+++ Lib/ntpath.py	(working copy)
@@ -78,6 +78,9 @@
     """Normalize case of pathname.
 
     Makes all characters lowercase and all slashes into backslashes."""
+    if not isinstance(s, (bytes, str)):
+        raise TypeError("normcase() argument must be str or bytes, "
+                        "not '{}'".format(s.__class__.__name__))
     return s.replace(_get_altsep(s), _get_sep(s)).lower()
 
 
Index: Lib/macpath.py
===================================================================
--- Lib/macpath.py	(revision 82145)
+++ Lib/macpath.py	(working copy)
@@ -32,6 +32,9 @@
 # Normalize the case of a pathname.  Dummy in Posix, but <s>.lower() here.
 
 def normcase(path):
+    if not isinstance(path, (bytes, str)):
+        raise TypeError("normcase() argument must be str or bytes, "
+                        "not '{}'".format(path.__class__.__name__))
     return path.lower()
 
 
Index: Lib/test/test_genericpath.py
===================================================================
--- Lib/test/test_genericpath.py	(revision 82145)
+++ Lib/test/test_genericpath.py	(working copy)
@@ -194,15 +194,23 @@
     ]
 
     def test_normcase(self):
-        # Check that normcase() is idempotent
+        normcase = self.pathmodule.normcase
+        # check that normcase() is idempotent
         p = "FoO/./BaR"
-        p = self.pathmodule.normcase(p)
+        p = normcase(p)
         self.assertEqual(p, self.pathmodule.normcase(p))
 
         p = b"FoO/./BaR"
-        p = self.pathmodule.normcase(p)
-        self.assertEqual(p, self.pathmodule.normcase(p))
+        p = normcase(p)
+        self.assertEqual(p, normcase(p))
 
+        self.assertEqual(normcase(''), '')
+        self.assertEqual(normcase(b''), b'')
+
+        # check that normcase raises a TypeError for invalid types
+        for path in (None, True, 0, 2.5, [], bytearray(b''), {'o','o'}):
+            self.assertRaises(TypeError, normcase, path)
+
     def test_splitdrive(self):
         # splitdrive for non-NT paths
         splitdrive = self.pathmodule.splitdrive