diff --git a/gymnasium/wrappers/stateful_observation.py b/gymnasium/wrappers/stateful_observation.py
index 9414ae17f..d593dc720 100644
--- a/gymnasium/wrappers/stateful_observation.py
+++ b/gymnasium/wrappers/stateful_observation.py
@@ -487,6 +487,7 @@ class NormalizeObservation(
     Change logs:
      * v0.21.0 - Initially add
      * v1.0.0 - Add `update_running_mean` attribute to allow disabling of updating the running mean / standard, particularly useful for evaluation time.
+        Casts all observations to `np.float32` and sets the observation space with low/high of `-np.inf` and `np.inf` and dtype as `np.float32`
     """
 
     def __init__(self, env: gym.Env[ObsType, ActType], epsilon: float = 1e-8):
@@ -499,6 +500,14 @@ class NormalizeObservation(
         gym.utils.RecordConstructorArgs.__init__(self, epsilon=epsilon)
         gym.ObservationWrapper.__init__(self, env)
 
+        assert env.observation_space.shape is not None
+        self.observation_space = gym.spaces.Box(
+            low=-np.inf,
+            high=np.inf,
+            shape=env.observation_space.shape,
+            dtype=np.float32,
+        )
+
         self.obs_rms = RunningMeanStd(
             shape=self.observation_space.shape, dtype=self.observation_space.dtype
         )
@@ -519,8 +528,8 @@ class NormalizeObservation(
         """Normalises the observation using the running mean and variance of the observations."""
         if self._update_running_mean:
             self.obs_rms.update(np.array([observation]))
-        return (observation - self.obs_rms.mean) / np.sqrt(
-            self.obs_rms.var + self.epsilon
+        return np.float32(
+            (observation - self.obs_rms.mean) / np.sqrt(self.obs_rms.var + self.epsilon)
         )
 
 
diff --git a/tests/wrappers/test_normalize_observation.py b/tests/wrappers/test_normalize_observation.py
index 0fff7a995..9639d4100 100644
--- a/tests/wrappers/test_normalize_observation.py
+++ b/tests/wrappers/test_normalize_observation.py
@@ -1,6 +1,7 @@
 """Test suite for NormalizeObservation wrapper."""
 import numpy as np
 
+import gymnasium as gym
 from gymnasium import spaces, wrappers
 from gymnasium.wrappers import NormalizeObservation
 from tests.testing_env import GenericTestEnv
@@ -62,3 +63,14 @@ def test_update_running_mean_property():
     wrapped_env.step(None)
     assert rms_var_updated == wrapped_env.obs_rms.var
     assert rms_mean_updated == wrapped_env.obs_rms.mean
+
+
+def test_normalize_obs_with_vector():
+    def thunk():
+        env = gym.make("CarRacing-v2")
+        env = gym.wrappers.GrayscaleObservation(env)
+        env = gym.wrappers.NormalizeObservation(env)
+        return env
+
+    envs = gym.vector.SyncVectorEnv([thunk for _ in range(4)])
+    obs, _ = envs.reset()