BUG: Fix assert_frame_equal with check_dtype=False for pd.NA with different dtypes

doc/source/whatsnew/v3.0.0.rst

@@ -955,6 +955,7 @@ Other
 ^^^^^
 - Bug in :class:`DataFrame` when passing a ``dict`` with a NA scalar and ``columns`` that would always return ``np.nan`` (:issue:`57205`)
 - Bug in :class:`Series` ignoring errors when trying to convert :class:`Series` input data to the given ``dtype`` (:issue:`60728`)
+- Bug in :func:`assert_frame_equal` with ``check_dtype=False`` failing to compare DataFrames containing ``pd.NA`` that differ only in dtype (``object`` vs ``Int32``). (:issue:`61473`)
 - Bug in :func:`eval` on :class:`ExtensionArray` on including division ``/`` failed with a ``TypeError``. (:issue:`58748`)
 - Bug in :func:`eval` where method calls on binary operations like ``(x + y).dropna()`` would raise ``AttributeError: 'BinOp' object has no attribute 'value'`` (:issue:`61175`)
 - Bug in :func:`eval` where the names of the :class:`Series` were not preserved when using ``engine="numexpr"``. (:issue:`10239`)

pandas/_testing/asserters.py

@@ -1031,10 +1031,16 @@ def assert_series_equal(
         else:
             # convert both to NumPy if not, check_dtype would raise earlier
             lv, rv = left_values, right_values
-            if isinstance(left_values, ExtensionArray):
-                lv = left_values.to_numpy()
-            if isinstance(right_values, ExtensionArray):
-                rv = right_values.to_numpy()
+            if check_dtype:
+                if isinstance(left_values, ExtensionArray):
+                    lv = left_values.to_numpy()
+                if isinstance(right_values, ExtensionArray):
+                    rv = right_values.to_numpy()
+            else:
+                if isinstance(left_values, ExtensionArray):
+                    lv = left_values.to_numpy(dtype="object")
+                if isinstance(right_values, ExtensionArray):
+                    rv = right_values.to_numpy(dtype="object")
             assert_numpy_array_equal(
                 lv,
                 rv,

pandas/tests/util/test_assert_frame_equal.py

@@ -395,3 +395,11 @@ def test_assert_frame_equal_set_mismatch():
     msg = r'DataFrame.iloc\[:, 0\] \(column name="set_column"\) values are different'
     with pytest.raises(AssertionError, match=msg):
         tm.assert_frame_equal(df1, df2)
+
+
+def test_assert_frame_equal_pdNa_ignore_dtype():
+    # GH#61473
+    df1 = DataFrame({"x": pd.Series([pd.NA], dtype="Int32")})
+    df2 = DataFrame({"x": pd.Series([pd.NA], dtype="object")})
+
+    tm.assert_frame_equal(df1, df2, check_dtype=False)