diff --git a/xarray/core/duck_array_ops.py b/xarray/core/duck_array_ops.py
index af5c415cdce..b30ba4c3a78 100644
--- a/xarray/core/duck_array_ops.py
+++ b/xarray/core/duck_array_ops.py
@@ -18,6 +18,7 @@
 from numpy import any as array_any  # noqa
 from numpy import (  # noqa
     around,  # noqa
+    full_like,
     gradient,
     isclose,
     isin,
@@ -26,7 +27,6 @@
     tensordot,
     transpose,
     unravel_index,
-    zeros_like,  # noqa
 )
 from numpy import concatenate as _concatenate
 from numpy.lib.stride_tricks import sliding_window_view  # noqa
@@ -151,7 +151,7 @@ def isnull(data):
         return xp.isnan(data)
     elif issubclass(scalar_type, (np.bool_, np.integer, np.character, np.void)):
         # these types cannot represent missing values
-        return zeros_like(data, dtype=bool)
+        return full_like(data, dtype=bool, fill_value=False)
     else:
         # at this point, array should have dtype=object
         if isinstance(data, np.ndarray):
diff --git a/xarray/tests/test_duck_array_ops.py b/xarray/tests/test_duck_array_ops.py
index 9167c2ddbea..7757ec58edc 100644
--- a/xarray/tests/test_duck_array_ops.py
+++ b/xarray/tests/test_duck_array_ops.py
@@ -577,17 +577,39 @@ def test_argmin_max_error():
 
 
 @pytest.mark.parametrize(
-    "array",
+    ["array", "expected"],
     [
-        np.array([np.datetime64("2000-01-01"), np.datetime64("NaT")]),
-        np.array([np.timedelta64(1, "h"), np.timedelta64("NaT")]),
-        np.array([0.0, np.nan]),
-        np.array([1j, np.nan]),
-        np.array(["foo", np.nan], dtype=object),
+        (
+            np.array([np.datetime64("2000-01-01"), np.datetime64("NaT")]),
+            np.array([False, True]),
+        ),
+        (
+            np.array([np.timedelta64(1, "h"), np.timedelta64("NaT")]),
+            np.array([False, True]),
+        ),
+        (
+            np.array([0.0, np.nan]),
+            np.array([False, True]),
+        ),
+        (
+            np.array([1j, np.nan]),
+            np.array([False, True]),
+        ),
+        (
+            np.array(["foo", np.nan], dtype=object),
+            np.array([False, True]),
+        ),
+        (
+            np.array([1, 2], dtype=int),
+            np.array([False, False]),
+        ),
+        (
+            np.array([True, False], dtype=bool),
+            np.array([False, False]),
+        ),
     ],
 )
-def test_isnull(array):
-    expected = np.array([False, True])
+def test_isnull(array, expected):
     actual = duck_array_ops.isnull(array)
     np.testing.assert_equal(expected, actual)