diff -r 9fb30d6af6a9 Lib/functools.py
--- a/Lib/functools.py	Tue Sep 06 21:12:44 2016 -0700
+++ b/Lib/functools.py	Wed Sep 07 17:38:20 2016 +0800
@@ -709,6 +709,8 @@
 
         """
         nonlocal cache_token
+        if not isinstance(cls, type):
+            raise TypeError("dispatch() argument must be a type")
         if cache_token is not None:
             current_token = get_cache_token()
             if cache_token != current_token:
@@ -731,6 +733,8 @@
 
         """
         nonlocal cache_token
+        if not isinstance(cls, type):
+            raise TypeError("register() argument must be a type")
         if func is None:
             return lambda f: register(cls, f)
         registry[cls] = func
diff -r 9fb30d6af6a9 Lib/test/test_functools.py
--- a/Lib/test/test_functools.py	Tue Sep 06 21:12:44 2016 -0700
+++ b/Lib/test/test_functools.py	Wed Sep 07 17:38:20 2016 +0800
@@ -1465,6 +1465,18 @@
 
 
 class TestSingleDispatch(unittest.TestCase):
+    def test_arguments_type(self):
+        # issue27984
+        from enum import Enum
+        IS = Enum("IS", "a, b")
+        @functools.singledispatch
+        def g(obj):
+            return "base"
+        with self.assertRaisesRegex(TypeError, "argument must be a type"):
+            g.register(IS.a)
+        with self.assertRaisesRegex(TypeError, "argument must be a type"):
+            g.dispatch(IS.b)
+
     def test_simple_overloads(self):
         @functools.singledispatch
         def g(obj):