diff --git a/jax/_src/pjit.py b/jax/_src/pjit.py
index faf1e9980..4c138fa85 100644
--- a/jax/_src/pjit.py
+++ b/jax/_src/pjit.py
@@ -223,7 +223,7 @@ def _get_states(attrs_tracked):
 
 def _get_fastpath_data(
     executable, out_tree, args_flat, out_flat, attrs_tracked, effects,
-    abstracted_axes
+    consts, abstracted_axes,
 ) -> Optional[pxla.MeshExecutableFastpathData]:
   out_reflattened, out_tree = pxla.reflatten_outputs_for_dispatch(out_tree, out_flat)
 
@@ -244,7 +244,7 @@ def _get_fastpath_data(
       # no prng reuse checking
       and not (config.debug_key_reuse.value and any(
         hasattr(arg, 'dtype') and dtypes.issubdtype(arg.dtype, dtypes.prng_key)
-        for arg in (*args_flat, *out_flat)))
+        for arg in (*args_flat, *out_flat, *consts)))
       )
 
   if use_fastpath:
@@ -306,7 +306,7 @@ def _cpp_pjit(jit_info: PjitInfo):
     executable = _read_most_recent_pjit_call_executable(jaxpr)
     maybe_fastpath_data = _get_fastpath_data(
         executable, out_tree, args_flat, out_flat, attrs_tracked, jaxpr.effects,
-        jit_info.abstracted_axes)
+        jaxpr.consts, jit_info.abstracted_axes)
     return outs, maybe_fastpath_data
 
   fun = jit_info.fun
@@ -1557,7 +1557,7 @@ def _pjit_call_impl(*args, jaxpr,
         inline=inline)
     fastpath_data = _get_fastpath_data(
         compiled, tree_structure(out_flat), args, out_flat, [], jaxpr.effects,
-        None)
+        jaxpr.consts, None)
     return out_flat, fastpath_data
 
   f = _get_jaxpr_as_fun(
diff --git a/jax/experimental/key_reuse/_core.py b/jax/experimental/key_reuse/_core.py
index 94ef166e6..5287a646d 100644
--- a/jax/experimental/key_reuse/_core.py
+++ b/jax/experimental/key_reuse/_core.py
@@ -356,14 +356,15 @@ def jaxpr_type_signature(jaxpr: core.Jaxpr) -> KeyReuseSignature:
           raise KeyReuseError(f"In {eqn.primitive}, source {src.idx} out of range [0, {len(eqn.outvars)}]")
         source(eqn.outvars[src.idx])
 
+  all_inputs = [*jaxpr.invars, *jaxpr.constvars]
   return KeyReuseSignature(
-    *(Sink(i, consumed[v]) for i, v in enumerate(jaxpr.invars)
+    *(Sink(i, consumed[v]) for i, v in enumerate(all_inputs)
       if is_key(v) and np.any(consumed.get(v, False))),
     *(Source(i) for i, v in enumerate(jaxpr.outvars)
-      if is_key(v) and resolve_forwards(v) not in jaxpr.invars and not consumed.get(v, False)),
-    *(Forward(jaxpr.invars.index(resolve_forwards(outvar)), idx_out)  # type: ignore[arg-type]
+      if is_key(v) and resolve_forwards(v) not in all_inputs and not consumed.get(v, False)),
+    *(Forward(all_inputs.index(resolve_forwards(outvar)), idx_out)  # type: ignore[arg-type]
       for idx_out, outvar in enumerate(jaxpr.outvars)
-      if is_key(outvar) and resolve_forwards(outvar) in jaxpr.invars)
+      if is_key(outvar) and resolve_forwards(outvar) in all_inputs)
   )
 
 
@@ -531,23 +532,24 @@ def key_reuse_impl_rule(prim, original_rule):
   @wraps(original_rule)
   def key_reuse_impl(*args, **kwargs):
     if config.debug_key_reuse.value:
+      funcname = str(prim)
+      jaxpr = None
+      consts = []
       if prim == pjit.pjit_p:
         funcname = "jit-compiled function"
         jaxpr = kwargs['jaxpr'].jaxpr
+        consts = kwargs['jaxpr'].consts
         signature = jaxpr_type_signature(jaxpr)
       elif prim in key_reuse_signatures:
-        funcname = str(prim)
-        jaxpr = None
         signature = key_reuse_signatures[prim]
       elif prim in key_reuse_signatures_dynamic:
-        funcname = str(prim)
         jaxpr = jax.make_jaxpr(partial(prim.bind, **kwargs))(*args).jaxpr
         signature = jaxpr_type_signature(jaxpr)
       else:
         raise RuntimeError(f"Internal: no key reuse rule for primitive {prim}")
-      signature.check_signature(*args, funcname=funcname)
+      signature.check_signature(*args, *consts, funcname=funcname)
       result =  original_rule(*args, **kwargs)
-      signature.update_consumption(args, result if prim.multiple_results else [result])
+      signature.update_consumption([*args, *consts], result if prim.multiple_results else [result])
       return result
     else:
       return original_rule(*args, **kwargs)
diff --git a/tests/key_reuse_test.py b/tests/key_reuse_test.py
index d98984be5..286088eeb 100644
--- a/tests/key_reuse_test.py
+++ b/tests/key_reuse_test.py
@@ -623,17 +623,26 @@ class KeyReuseEagerTest(jtu.JaxTestCase):
 
   def test_simple_reuse_nojit(self):
     key = jax.random.key(0)
-    _ = jax.random.bits(key)
     with jax.disable_jit():
+      _ = jax.random.bits(key)
       with self.assertRaisesRegex(KeyReuseError, self.eager_bits_msg):
         _ = jax.random.bits(key)
 
   def test_simple_key_reuse_jit(self):
     key = jax.random.key(0)
-    _ = jax.random.bits(key)
+    _ = jax.jit(jax.random.bits)(key)
     with self.assertRaisesRegex(KeyReuseError, self.jit_msg):
       _ = jax.jit(jax.random.bits)(key)
 
+  def test_closed_over_key_reuse_jit(self):
+    key = jax.random.key(0)
+    @jax.jit
+    def f():
+      return jax.random.uniform(key)
+    _ = f()
+    with self.assertRaisesRegex(KeyReuseError, self.jit_msg):
+      _ = f()
+
   def test_key_reuse_within_jit(self):
     @jax.jit
     def f():