Update test_arrow.py

added test case

Author: road-1

pandas/tests/extension/test_arrow.py

@@ -3507,3 +3507,13 @@ def test_map_numeric_na_action():
     result = ser.map(lambda x: 42, na_action="ignore")
     expected = pd.Series([42.0, 42.0, np.nan], dtype="float64")
     tm.assert_series_equal(result, expected)
+
+def test_convert_dtypes_timezone_series():
+    # GH#60237
+    ser = pd.Series(pd.date_range(start='2020-01-01', 
+                                periods=5, freq='h', 
+                                tz='UTC'), 
+                                dtype="timestamp[ns, tz=UTC][pyarrow]")
+    expected = ser
+    result = ser.convert_dtypes(dtype_backend="pyarrow")
+    tm.assert_series_equal(result, expected)