diff --git a/cubed/tests/test_array_api.py b/cubed/tests/test_array_api.py
index 8500b4d7..b8c68dbe 100644
--- a/cubed/tests/test_array_api.py
+++ b/cubed/tests/test_array_api.py
@@ -424,11 +424,13 @@ def test_outer(spec, executor):
 
 
 @pytest.mark.parametrize("axes", [1, (1, 0)])
-def test_tensordot(axes):
-    x = np.arange(400, dtype=np.float32).reshape((20, 20))
-    a = xp.asarray(x, chunks=(5, 4), dtype=xp.float32)
-    y = np.arange(200, dtype=np.float32).reshape((20, 10))
-    b = xp.asarray(y, chunks=(4, 5), dtype=xp.float32)
+@pytest.mark.parametrize("dtypes", [(None, None), (np.float32, xp.float32)])
+def test_tensordot(axes, dtypes):
+    ntype, xtype = dtypes
+    x = np.arange(400, dtype=ntype).reshape((20, 20))
+    a = xp.asarray(x, chunks=(5, 4), dtype=xtype)
+    y = np.arange(200, dtype=ntype).reshape((20, 10))
+    b = xp.asarray(y, chunks=(4, 5), dtype=xtype)
     assert_array_equal(
         xp.tensordot(a, b, axes=axes).compute(), np.tensordot(x, y, axes=axes)
     )