BUG: Have object dtype for empty Categorical ctor

Previously we had a `Float64Index`, which is inconsistent with, e.g., the
regular Index constructor.

doc/source/whatsnew/v0.21.0.txt

@@ -379,6 +379,9 @@ Numeric
 Categorical
 ^^^^^^^^^^^
 - Bug in :func:`Series.isin` when called with a categorical (:issue`16639`)
+- Bug in the categorical constructor with empty values and categories causing
+  the ``.categories`` to be an empty ``Float64Index`` rather than an empty
+  ``Index`` with object dtype (:issue:`17248`)
 
 
 Other

pandas/core/categorical.py

@@ -290,7 +290,10 @@ def __init__(self, values, categories=None, ordered=False, fastpath=False):
                 # On list with NaNs, int values will be converted to float. Use
                 # "object" dtype to prevent this. In the end objects will be
                 # casted to int/... in the category assignment step.
-                dtype = 'object' if isna(values).any() else None
+                if len(values) == 0 or isna(values).any():
+                    dtype = 'object'
+                else:
+                    dtype = None
                 values = _sanitize_array(values, None, dtype=dtype)
 
         if categories is None:

pandas/tests/test_categorical.py

@@ -112,6 +112,16 @@ def test_setitem_listlike(self):
         result = c.codes[np.array([100000]).astype(np.int64)]
         tm.assert_numpy_array_equal(result, np.array([5], dtype='int8'))
 
+    def test_constructor_empty(self):
+        # GH 17248
+        c = Categorical([])
+        expected = Index([])
+        tm.assert_index_equal(c.categories, expected)
+
+        c = Categorical([], categories=[1, 2, 3])
+        expected = pd.Int64Index([1, 2, 3])
+        tm.assert_index_equal(c.categories, expected)
+
     def test_constructor_unsortable(self):
 
         # it works!