diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index b10f201e79318..850391522dbff 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -225,6 +225,7 @@ Copy-on-Write improvements
   - :meth:`DataFrame.tz_convert` / :meth:`Series.tz_localize`
   - :meth:`DataFrame.infer_objects` / :meth:`Series.infer_objects`
   - :meth:`DataFrame.astype` / :meth:`Series.astype`
+  - :meth:`DataFrame.convert_dtypes` / :meth:`Series.convert_dtypes`
   - :func:`concat`
 
   These methods return views when Copy-on-Write is enabled, which provides a significant
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index aaf1d0e022fdf..1b96ff57a6efc 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -6642,7 +6642,7 @@ def convert_dtypes(
                 # https://github.com/python/mypy/issues/8354
                 return cast(NDFrameT, result)
             else:
-                return self.copy()
+                return self.copy(deep=None)
 
     # ----------------------------------------------------------------------
     # Filling NA's
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 80dd0dd19f96f..a88dd224068ac 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -5468,7 +5468,7 @@ def _convert_dtypes(
         if infer_objects:
             input_series = input_series.infer_objects()
             if is_object_dtype(input_series):
-                input_series = input_series.copy()
+                input_series = input_series.copy(deep=None)
 
         if convert_string or convert_integer or convert_boolean or convert_floating:
             dtype_backend = get_option("mode.dtype_backend")
@@ -5483,7 +5483,7 @@ def _convert_dtypes(
             )
             result = input_series.astype(inferred_dtype)
         else:
-            result = input_series.copy()
+            result = input_series.copy(deep=None)
         return result
 
     # error: Cannot determine type of 'isna'
diff --git a/pandas/tests/copy_view/test_astype.py b/pandas/tests/copy_view/test_astype.py
index a485275a28ac4..73343976e92fb 100644
--- a/pandas/tests/copy_view/test_astype.py
+++ b/pandas/tests/copy_view/test_astype.py
@@ -193,3 +193,42 @@ def test_astype_arrow_timestamp(using_copy_on_write):
     if using_copy_on_write:
         assert not result._mgr._has_no_reference(0)
         assert np.shares_memory(get_array(df, "a").asi8, get_array(result, "a")._data)
+
+
+def test_convert_dtypes_infer_objects(using_copy_on_write):
+    ser = Series(["a", "b", "c"])
+    ser_orig = ser.copy()
+    result = ser.convert_dtypes(
+        convert_integer=False,
+        convert_boolean=False,
+        convert_floating=False,
+        convert_string=False,
+    )
+
+    if using_copy_on_write:
+        assert np.shares_memory(get_array(ser), get_array(result))
+    else:
+        assert not np.shares_memory(get_array(ser), get_array(result))
+
+    result.iloc[0] = "x"
+    tm.assert_series_equal(ser, ser_orig)
+
+
+def test_convert_dtypes(using_copy_on_write):
+    df = DataFrame({"a": ["a", "b"], "b": [1, 2], "c": [1.5, 2.5], "d": [True, False]})
+    df_orig = df.copy()
+    df2 = df.convert_dtypes()
+
+    if using_copy_on_write:
+        assert np.shares_memory(get_array(df2, "a"), get_array(df, "a"))
+        assert np.shares_memory(get_array(df2, "d"), get_array(df, "d"))
+        assert np.shares_memory(get_array(df2, "b"), get_array(df, "b"))
+        assert np.shares_memory(get_array(df2, "c"), get_array(df, "c"))
+    else:
+        assert not np.shares_memory(get_array(df2, "a"), get_array(df, "a"))
+        assert not np.shares_memory(get_array(df2, "b"), get_array(df, "b"))
+        assert not np.shares_memory(get_array(df2, "c"), get_array(df, "c"))
+        assert not np.shares_memory(get_array(df2, "d"), get_array(df, "d"))
+
+    df2.iloc[0, 0] = "x"
+    tm.assert_frame_equal(df, df_orig)
diff --git a/pandas/tests/copy_view/util.py b/pandas/tests/copy_view/util.py
index b5f4f74fc7e5e..8e53c1644b0a2 100644
--- a/pandas/tests/copy_view/util.py
+++ b/pandas/tests/copy_view/util.py
@@ -2,7 +2,7 @@
 from pandas.core.arrays import BaseMaskedArray
 
 
-def get_array(obj, col):
+def get_array(obj, col=None):
     """
     Helper method to get array for a DataFrame column or a Series.
 
@@ -10,8 +10,9 @@ def get_array(obj, col):
     which triggers tracking references / CoW (and we might be testing that
     this is done by some other operation).
     """
-    if isinstance(obj, Series) and obj.name == col:
+    if isinstance(obj, Series) and (obj is None or obj.name == col):
         return obj._values
+    assert col is not None
     icol = obj.columns.get_loc(col)
     assert isinstance(icol, int)
     arr = obj._get_column_array(icol)