BUG: CoW not tracking references when indexing midx with slice (#51944)

doc/source/whatsnew/v2.0.0.rst

@@ -206,6 +206,9 @@ Copy-on-Write improvements
 - Arithmetic operations that can be inplace, e.g. ``ser *= 2`` will now respect the
   Copy-on-Write mechanism.
 
+- :meth:`DataFrame.__getitem__` will now respect the Copy-on-Write mechanism when the
+  :class:`DataFrame` has :class:`MultiIndex` columns.
+
 - :meth:`Series.view` will now respect the Copy-on-Write mechanism.
 
 Copy-on-Write can be enabled through one of

pandas/core/frame.py

@@ -3832,10 +3832,13 @@ def _getitem_multilevel(self, key):
                 result = self.reindex(columns=new_columns)
                 result.columns = result_columns
             else:
-                new_values = self.values[:, loc]
+                new_values = self._values[:, loc]
                 result = self._constructor(
                     new_values, index=self.index, columns=result_columns
                 )
+                if using_copy_on_write() and isinstance(loc, slice):
+                    result._mgr.add_references(self._mgr)  # type: ignore[arg-type]
+
                 result = result.__finalize__(self)
 
             # If there is only one column being returned, and its name is

pandas/tests/copy_view/test_indexing.py

@@ -1034,3 +1034,18 @@ def test_set_value_copy_only_necessary_column(
             assert not np.shares_memory(get_array(df, "a"), get_array(view, "a"))
         else:
             assert np.shares_memory(get_array(df, "a"), get_array(view, "a"))
+
+
+def test_getitem_midx_slice(using_copy_on_write, using_array_manager):
+    df = DataFrame({("a", "x"): [1, 2], ("a", "y"): 1, ("b", "x"): 2})
+    df_orig = df.copy()
+    new_df = df[("a",)]
+
+    if using_copy_on_write:
+        assert not new_df._mgr._has_no_reference(0)
+
+    if not using_array_manager:
+        assert np.shares_memory(get_array(df, ("a", "x")), get_array(new_df, "x"))
+    if using_copy_on_write:
+        new_df.iloc[0, 0] = 100
+        tm.assert_frame_equal(df_orig, df)