diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 95804de2a7089..2c66b0c67c3dd 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -405,6 +405,8 @@ def set_flags(
 
         Parameters
         ----------
+        copy : bool, default False
+            Specify if a copy of the object should be made.
         allows_duplicate_labels : bool, optional
             Whether the returned object allows duplicate labels.
 
diff --git a/pandas/tests/copy_view/test_methods.py b/pandas/tests/copy_view/test_methods.py
index 2b3d13b982d4d..9e3d8f8076be1 100644
--- a/pandas/tests/copy_view/test_methods.py
+++ b/pandas/tests/copy_view/test_methods.py
@@ -500,6 +500,24 @@ def test_series_set_axis(using_copy_on_write):
     tm.assert_series_equal(ser, ser_orig)
 
 
+def test_set_flags(using_copy_on_write):
+    ser = Series([1, 2, 3])
+    ser_orig = ser.copy()
+    ser2 = ser.set_flags(allows_duplicate_labels=False)
+
+    assert np.shares_memory(ser, ser2)
+
+    # mutating ser triggers a copy-on-write for the column / block
+    ser2.iloc[0] = 0
+    if using_copy_on_write:
+        assert not np.shares_memory(ser2, ser)
+        tm.assert_series_equal(ser, ser_orig)
+    else:
+        assert np.shares_memory(ser2, ser)
+        expected = Series([0, 2, 3])
+        tm.assert_series_equal(ser, expected)
+
+
 @pytest.mark.parametrize("copy_kwargs", [{"copy": True}, {}])
 @pytest.mark.parametrize("kwargs", [{"mapper": "test"}, {"index": "test"}])
 def test_rename_axis(using_copy_on_write, kwargs, copy_kwargs):