diff --git a/tests/dispatch/test_jax.py b/tests/dispatch/test_jax.py
new file mode 100644
index 0000000000..67aa695910
--- /dev/null
+++ b/tests/dispatch/test_jax.py
@@ -0,0 +1,36 @@
+#   Copyright 2024 The PyMC Developers
+#
+#   Licensed under the Apache License, Version 2.0 (the "License");
+#   you may not use this file except in compliance with the License.
+#   You may obtain a copy of the License at
+#
+#       http://www.apache.org/licenses/LICENSE-2.0
+#
+#   Unless required by applicable law or agreed to in writing, software
+#   distributed under the License is distributed on an "AS IS" BASIS,
+#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+#   See the License for the specific language governing permissions and
+#   limitations under the License.
+import numpy as np
+import pytest
+
+from pytensor import function
+
+import pymc as pm
+
+jax = pytest.importorskip("jax", reason="JAX is not installed")
+
+
+def test_jax_TruncatedNormal():
+    with pm.Model() as m:
+        f_jax = function(
+            [],
+            [pm.TruncatedNormal("a", 0, 1, lower=-1, upper=2, rng=np.random.default_rng(seed=123))],
+            mode="JAX",
+        )
+        f_py = function(
+            [],
+            [pm.TruncatedNormal("b", 0, 1, lower=-1, upper=2, rng=np.random.default_rng(seed=123))],
+        )
+
+    assert jax.numpy.array_equal(a1=f_py(), a2=f_jax())