diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index 9ceb50611f1c5..e4c5541468629 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -1750,7 +1750,9 @@ def objs_to_bool(vals: ArrayLike) -> tuple[np.ndarray, type]:
             if is_object_dtype(vals.dtype):
                 # GH#37501: don't raise on pd.NA when skipna=True
                 if skipna:
-                    func = np.vectorize(lambda x: bool(x) if not isna(x) else True)
+                    func = np.vectorize(
+                        lambda x: bool(x) if not isna(x) else True, otypes=[bool]
+                    )
                     vals = func(vals)
                 else:
                     vals = vals.astype(bool, copy=False)
diff --git a/pandas/tests/groupby/test_any_all.py b/pandas/tests/groupby/test_any_all.py
index 13232d454a48c..3f61a4ece66c0 100644
--- a/pandas/tests/groupby/test_any_all.py
+++ b/pandas/tests/groupby/test_any_all.py
@@ -178,3 +178,13 @@ def test_object_NA_raises_with_skipna_false(bool_agg_func):
     ser = Series([pd.NA], dtype=object)
     with pytest.raises(TypeError, match="boolean value of NA is ambiguous"):
         ser.groupby([1]).agg(bool_agg_func, skipna=False)
+
+
+@pytest.mark.parametrize("bool_agg_func", ["any", "all"])
+def test_empty(frame_or_series, bool_agg_func):
+    # GH 45231
+    kwargs = {"columns": ["a"]} if frame_or_series is DataFrame else {"name": "a"}
+    obj = frame_or_series(**kwargs, dtype=object)
+    result = getattr(obj.groupby(obj.index), bool_agg_func)()
+    expected = frame_or_series(**kwargs, dtype=bool)
+    tm.assert_equal(result, expected)