diff --git a/src/neo4j/_async/driver.py b/src/neo4j/_async/driver.py
index 4a2c0a1df..cc923b553 100644
--- a/src/neo4j/_async/driver.py
+++ b/src/neo4j/_async/driver.py
@@ -563,7 +563,9 @@ def _prepare_session_config(cls, preview_check, config_kwargs):
     async def close(self) -> None:
         """ Shut down, closing any open connections in the pool.
         """
-        self._check_state()
+        # TODO: 6.0 - NOOP if already closed
+        # if self._closed:
+        #     return
         try:
             await self._pool.close()
         except asyncio.CancelledError:
diff --git a/src/neo4j/_sync/driver.py b/src/neo4j/_sync/driver.py
index cad5f0442..754c2138c 100644
--- a/src/neo4j/_sync/driver.py
+++ b/src/neo4j/_sync/driver.py
@@ -562,7 +562,9 @@ def _prepare_session_config(cls, preview_check, config_kwargs):
     def close(self) -> None:
         """ Shut down, closing any open connections in the pool.
         """
-        self._check_state()
+        # TODO: 6.0 - NOOP if already closed
+        # if self._closed:
+        #     return
         try:
             self._pool.close()
         except asyncio.CancelledError:
diff --git a/tests/unit/async_/test_driver.py b/tests/unit/async_/test_driver.py
index ea11f43be..e65e456f4 100644
--- a/tests/unit/async_/test_driver.py
+++ b/tests/unit/async_/test_driver.py
@@ -21,6 +21,7 @@
 import inspect
 import ssl
 import typing as t
+import warnings
 
 import pytest
 import typing_extensions as te
@@ -963,12 +964,11 @@ async def test_supports_session_auth(session_cls_mock) -> None:
         ("get_server_info", (), {}),
         ("supports_multi_db", (), {}),
         ("supports_session_auth", (), {}),
-        ("close", (), {}),
 
     )
 )
 @mark_async_test
-async def test_using_closed_driver_is_deprecated(
+async def test_using_closed_driver_where_deprecated(
     method_name, args, kwargs, session_cls_mock
 ) -> None:
     driver = AsyncGraphDatabase.driver("bolt://localhost")
@@ -983,3 +983,25 @@ async def test_using_closed_driver_is_deprecated(
             await method(*args, **kwargs)
         else:
             method(*args, **kwargs)
+
+
+@pytest.mark.parametrize(
+    ("method_name", "args", "kwargs"),
+    (
+        ("close", (), {}),
+    )
+)
+@mark_async_test
+async def test_using_closed_driver_where_not_deprecated(
+    method_name, args, kwargs, session_cls_mock
+) -> None:
+    driver = AsyncGraphDatabase.driver("bolt://localhost")
+    await driver.close()
+
+    method = getattr(driver, method_name)
+    with warnings.catch_warnings():
+        warnings.simplefilter("error")
+        if inspect.iscoroutinefunction(method):
+            await method(*args, **kwargs)
+        else:
+            method(*args, **kwargs)
diff --git a/tests/unit/sync/test_driver.py b/tests/unit/sync/test_driver.py
index c05c821ce..18e1afa69 100644
--- a/tests/unit/sync/test_driver.py
+++ b/tests/unit/sync/test_driver.py
@@ -21,6 +21,7 @@
 import inspect
 import ssl
 import typing as t
+import warnings
 
 import pytest
 import typing_extensions as te
@@ -962,12 +963,11 @@ def test_supports_session_auth(session_cls_mock) -> None:
         ("get_server_info", (), {}),
         ("supports_multi_db", (), {}),
         ("supports_session_auth", (), {}),
-        ("close", (), {}),
 
     )
 )
 @mark_sync_test
-def test_using_closed_driver_is_deprecated(
+def test_using_closed_driver_where_deprecated(
     method_name, args, kwargs, session_cls_mock
 ) -> None:
     driver = GraphDatabase.driver("bolt://localhost")
@@ -982,3 +982,25 @@ def test_using_closed_driver_is_deprecated(
             method(*args, **kwargs)
         else:
             method(*args, **kwargs)
+
+
+@pytest.mark.parametrize(
+    ("method_name", "args", "kwargs"),
+    (
+        ("close", (), {}),
+    )
+)
+@mark_sync_test
+def test_using_closed_driver_where_not_deprecated(
+    method_name, args, kwargs, session_cls_mock
+) -> None:
+    driver = GraphDatabase.driver("bolt://localhost")
+    driver.close()
+
+    method = getattr(driver, method_name)
+    with warnings.catch_warnings():
+        warnings.simplefilter("error")
+        if inspect.iscoroutinefunction(method):
+            method(*args, **kwargs)
+        else:
+            method(*args, **kwargs)