BUG: is_string_dtype(pd.Index([], dtype='O')) returns False (#54997)

* correct def is_all_strings

* add a test, correct whatsnew/v2.2.0.rst

* move the test and add parametrization, correct v2.2.0.rst

* remove the line from v2.2.0.rst

* add the note to v2.1.1.rst

* correct the whatsnew note and move it to 2.2.0

doc/source/whatsnew/v2.2.0.rst

@@ -279,6 +279,7 @@ Bug fixes
 ~~~~~~~~~
 - Bug in :class:`AbstractHolidayCalendar` where timezone data was not propagated when computing holiday observances (:issue:`54580`)
 - Bug in :class:`pandas.core.window.Rolling` where duplicate datetimelike indexes are treated as consecutive rather than equal with ``closed='left'`` and ``closed='neither'`` (:issue:`20712`)
+- Bug in :func:`pandas.api.types.is_string_dtype` while checking object array with no elements is of the string dtype (:issue:`54661`)
 - Bug in :meth:`DataFrame.apply` where passing ``raw=True`` ignored ``args`` passed to the applied function (:issue:`55009`)
 - Bug in :meth:`pandas.DataFrame.melt` where it would not preserve the datetime (:issue:`55254`)
 - Bug in :meth:`pandas.read_excel` with a ODS file without cached formatted cell for float values (:issue:`55219`)

pandas/core/dtypes/common.py

@@ -1664,9 +1664,12 @@ def is_all_strings(value: ArrayLike) -> bool:
     dtype = value.dtype
 
     if isinstance(dtype, np.dtype):
-        return dtype == np.dtype("object") and lib.is_string_array(
-            np.asarray(value), skipna=False
-        )
+        if len(value) == 0:
+            return dtype == np.dtype("object")
+        else:
+            return dtype == np.dtype("object") and lib.is_string_array(
+                np.asarray(value), skipna=False
+            )
     elif isinstance(dtype, CategoricalDtype):
         return dtype.categories.inferred_type == "string"
     return dtype == "string"

pandas/tests/dtypes/test_common.py

@@ -301,14 +301,23 @@ def test_is_categorical_dtype():
         assert com.is_categorical_dtype(pd.CategoricalIndex([1, 2, 3]))
 
 
-def test_is_string_dtype():
-    assert not com.is_string_dtype(int)
-    assert not com.is_string_dtype(pd.Series([1, 2]))
-
-    assert com.is_string_dtype(str)
-    assert com.is_string_dtype(object)
-    assert com.is_string_dtype(np.array(["a", "b"]))
-    assert com.is_string_dtype(pd.StringDtype())
+@pytest.mark.parametrize(
+    "dtype, expected",
+    [
+        (int, False),
+        (pd.Series([1, 2]), False),
+        (str, True),
+        (object, True),
+        (np.array(["a", "b"]), True),
+        (pd.StringDtype(), True),
+        (pd.Index([], dtype="O"), True),
+    ],
+)
+def test_is_string_dtype(dtype, expected):
+    # GH#54661
+
+    result = com.is_string_dtype(dtype)
+    assert result is expected
 
 
 @pytest.mark.parametrize(