diff --git a/src/libtmux/session.py b/src/libtmux/session.py
index cc8725f98..b28cbb28f 100644
--- a/src/libtmux/session.py
+++ b/src/libtmux/session.py
@@ -531,8 +531,9 @@ def kill_window(self, target_window: t.Optional[t.Union[str, int]] = None) -> No
 
         Parameters
         ----------
-        target_window : str, optional
-            window to kill
+        target_window : str, int, optional
+            window to kill. Stands for a window id in the format "@{id}", 
+            if str, a window index if int, and an attached window if none.
         """
 
         kill_cmd = ["kill-window"]
diff --git a/tests/test_session.py b/tests/test_session.py
index 70100008e..386f0d816 100644
--- a/tests/test_session.py
+++ b/tests/test_session.py
@@ -323,6 +323,7 @@ def test_new_window_with_environment_logs_warning_for_old_tmux(
         "Cannot set up environment" in record.msg for record in caplog.records
     ), "Warning missing"
 
+
 @pytest.mark.parametrize(
     "target_window_mapper",
     [
@@ -334,7 +335,7 @@ def test_new_window_with_environment_logs_warning_for_old_tmux(
 def test_kill_window_by_id(
     session: Session, 
     target_window_mapper: t.Callable[[Window], t.Optional[t.Union[int, str]]],
-):
+) -> None:
     # kill by window index
     session.new_window()
     w = session.attached_window