diff --git a/torch_np/tests/test_dtype.py b/torch_np/tests/test_dtype.py
new file mode 100644
index 00000000..76392abb
--- /dev/null
+++ b/torch_np/tests/test_dtype.py
@@ -0,0 +1,51 @@
+import numpy as np
+import pytest
+
+import torch_np as tnp
+
+dtype_names = [
+    "bool_",
+    *[f"int{w}" for w in [8, 16, 32, 64]],
+    "uint8",
+    *[f"float{w}" for w in [16, 32, 64]],
+    *[f"complex{w}" for w in [64, 128]],
+]
+np_dtype_params = []
+np_dtype_params.append(pytest.param("bool", "bool", id="'bool'"))
+np_dtype_params.append(
+    pytest.param(
+        "bool",
+        np.dtype("bool"),
+        id=f"np.dtype('bool')",
+        marks=pytest.mark.xfail(reason="XXX: np.dtype() objects not supported"),
+    )
+)
+for name in dtype_names:
+    np_dtype_params.append(pytest.param(name, name, id=repr(name)))
+    np_dtype_params.append(
+        pytest.param(
+            name,
+            getattr(np, name),
+            id=f"np.{name}",
+            marks=pytest.mark.xfail(reason="XXX: namespaced dtypes not supported"),
+        )
+    )
+    np_dtype_params.append(
+        pytest.param(
+            name,
+            np.dtype(name),
+            id=f"np.dtype({name!r})",
+            marks=pytest.mark.xfail(reason="XXX: np.dtype() objects not supported"),
+        )
+    )
+
+
+@pytest.mark.parametrize("name, np_dtype", np_dtype_params)
+def test_convert_np_dtypes(name, np_dtype):
+    tnp_dtype = tnp.dtype(np_dtype)
+    if name == "bool_":
+        assert tnp_dtype == tnp.bool_
+    elif tnp_dtype.name == "bool_":
+        assert name.startswith("bool")
+    else:
+        assert tnp_dtype.name == name
diff --git a/torch_np/tests/test_xps.py b/torch_np/tests/test_xps.py
index 10700092..1d434ce9 100644
--- a/torch_np/tests/test_xps.py
+++ b/torch_np/tests/test_xps.py
@@ -144,3 +144,13 @@ def test_put(np_x, data):
     note(f"(after put) {tnp_x=}")
 
     assert_array_equal(tnp_x, tnp.asarray(np_x).astype(tnp_x.dtype))
+
+
+@pytest.mark.xfail(reason="XXX: support converting namespaced dtypes")
+@given(a=nps.arrays(dtype=nps.scalar_dtypes(), shape=nps.array_shapes()))
+def test_asarray_np_arrays(a):
+    x = tnp.asarray(a)
+    if a.dtype == np.bool_:
+        assert x.dtype == tnp.bool
+    else:
+        assert x.dtype.name == a.dtype.name