diff --git a/doc/source/whatsnew/v1.1.3.rst b/doc/source/whatsnew/v1.1.3.rst
index e3161012da5d1..c06990e3f2051 100644
--- a/doc/source/whatsnew/v1.1.3.rst
+++ b/doc/source/whatsnew/v1.1.3.rst
@@ -22,7 +22,7 @@ Fixed regressions
 
 Bug fixes
 ~~~~~~~~~
--
+- Bug in :meth:`Series.str.startswith` and :meth:`Series.str.endswith` with ``category`` dtype not propagating ``na`` parameter (:issue:`36241`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/core/strings.py b/pandas/core/strings.py
index 6702bf519c52e..4decd86764ccc 100644
--- a/pandas/core/strings.py
+++ b/pandas/core/strings.py
@@ -2050,7 +2050,7 @@ def wrapper2(self, pat, flags=0, **kwargs):
     @forbid_nonstring_types(forbidden_types, name=name)
     def wrapper3(self, pat, na=np.nan):
         result = f(self._parent, pat, na=na)
-        return self._wrap_result(result, returns_string=returns_string)
+        return self._wrap_result(result, returns_string=returns_string, fill_value=na)
 
     wrapper = wrapper3 if na else wrapper2 if flags else wrapper1
 
diff --git a/pandas/tests/test_strings.py b/pandas/tests/test_strings.py
index d9396d70f9112..c792a48d3ef08 100644
--- a/pandas/tests/test_strings.py
+++ b/pandas/tests/test_strings.py
@@ -29,6 +29,8 @@ def assert_series_or_index_equal(left, right):
     ("decode", ("UTF-8",), {}),
     ("encode", ("UTF-8",), {}),
     ("endswith", ("a",), {}),
+    ("endswith", ("a",), {"na": True}),
+    ("endswith", ("a",), {"na": False}),
     ("extract", ("([a-z]*)",), {"expand": False}),
     ("extract", ("([a-z]*)",), {"expand": True}),
     ("extractall", ("([a-z]*)",), {}),
@@ -58,6 +60,8 @@ def assert_series_or_index_equal(left, right):
     ("split", (" ",), {"expand": False}),
     ("split", (" ",), {"expand": True}),
     ("startswith", ("a",), {}),
+    ("startswith", ("a",), {"na": True}),
+    ("startswith", ("a",), {"na": False}),
     # translating unicode points of "a" to "d"
     ("translate", ({97: 100},), {}),
     ("wrap", (2,), {}),
@@ -838,15 +842,23 @@ def test_contains_for_object_category(self):
         expected = Series([True, False, False, True, False])
         tm.assert_series_equal(result, expected)
 
-    def test_startswith(self):
-        values = Series(["om", np.nan, "foo_nom", "nom", "bar_foo", np.nan, "foo"])
+    @pytest.mark.parametrize("dtype", [None, "category"])
+    @pytest.mark.parametrize("null_value", [None, np.nan, pd.NA])
+    @pytest.mark.parametrize("na", [True, False])
+    def test_startswith(self, dtype, null_value, na):
+        # add category dtype parametrizations for GH-36241
+        values = Series(
+            ["om", null_value, "foo_nom", "nom", "bar_foo", null_value, "foo"],
+            dtype=dtype,
+        )
 
         result = values.str.startswith("foo")
         exp = Series([False, np.nan, True, False, False, np.nan, True])
         tm.assert_series_equal(result, exp)
 
-        result = values.str.startswith("foo", na=True)
-        tm.assert_series_equal(result, exp.fillna(True).astype(bool))
+        result = values.str.startswith("foo", na=na)
+        exp = Series([False, na, True, False, False, na, True])
+        tm.assert_series_equal(result, exp)
 
         # mixed
         mixed = np.array(
@@ -867,15 +879,23 @@ def test_startswith(self):
         )
         tm.assert_series_equal(rs, xp)
 
-    def test_endswith(self):
-        values = Series(["om", np.nan, "foo_nom", "nom", "bar_foo", np.nan, "foo"])
+    @pytest.mark.parametrize("dtype", [None, "category"])
+    @pytest.mark.parametrize("null_value", [None, np.nan, pd.NA])
+    @pytest.mark.parametrize("na", [True, False])
+    def test_endswith(self, dtype, null_value, na):
+        # add category dtype parametrizations for GH-36241
+        values = Series(
+            ["om", null_value, "foo_nom", "nom", "bar_foo", null_value, "foo"],
+            dtype=dtype,
+        )
 
         result = values.str.endswith("foo")
         exp = Series([False, np.nan, False, False, True, np.nan, True])
         tm.assert_series_equal(result, exp)
 
-        result = values.str.endswith("foo", na=False)
-        tm.assert_series_equal(result, exp.fillna(False).astype(bool))
+        result = values.str.endswith("foo", na=na)
+        exp = Series([False, na, False, False, True, na, True])
+        tm.assert_series_equal(result, exp)
 
         # mixed
         mixed = np.array(
@@ -3552,6 +3572,10 @@ def test_string_array(any_string_method):
             assert result.dtype == "boolean"
             result = result.astype(object)
 
+        elif expected.dtype == "bool":
+            assert result.dtype == "boolean"
+            result = result.astype("bool")
+
         elif expected.dtype == "float" and expected.isna().any():
             assert result.dtype == "Int64"
             result = result.astype("float")