BUG: Avoid duplicates in DatetimeIndex.intersection (#38196)

Author: phofl

pandas/core/indexes/datetimelike.py

@@ -689,6 +689,8 @@ def intersection(self, other, sort=False):
         other, _ = self._convert_can_do_setop(other)
 
         if self.equals(other):
+            if self.has_duplicates:
+                return self.unique()._get_reconciled_name_object(other)
             return self._get_reconciled_name_object(other)
 
         return self._intersection(other, sort=sort)

pandas/tests/indexes/datetimes/test_setops.py

@@ -510,6 +510,20 @@ def test_month_range_union_tz_dateutil(self, sort):
 
         early_dr.union(late_dr, sort=sort)
 
+    @pytest.mark.parametrize("sort", [False, None])
+    def test_intersection_duplicates(self, sort):
+        # GH#38196
+        idx1 = Index(
+            [
+                pd.Timestamp("2019-12-13"),
+                pd.Timestamp("2019-12-12"),
+                pd.Timestamp("2019-12-12"),
+            ]
+        )
+        result = idx1.intersection(idx1, sort=sort)
+        expected = Index([pd.Timestamp("2019-12-13"), pd.Timestamp("2019-12-12")])
+        tm.assert_index_equal(result, expected)
+
 
 class TestCustomDatetimeIndex:
     def setup_method(self, method):