diff --git a/src/langchain_google_cloud_sql_pg/engine.py b/src/langchain_google_cloud_sql_pg/engine.py
index 102467bd..f1adc95e 100644
--- a/src/langchain_google_cloud_sql_pg/engine.py
+++ b/src/langchain_google_cloud_sql_pg/engine.py
@@ -82,7 +82,18 @@ async def _get_iam_principal_email(
 class PostgresEngine(PGEngine):
     """A class for managing connections to a Cloud SQL for Postgres database."""
 
-    _connector: Optional[Connector] = None
+    def __init__(
+        self,
+        key: object,
+        pool: AsyncEngine,
+        loop: Optional[asyncio.AbstractEventLoop] = None,
+        thread: Optional[Thread] = None,
+        connector: Optional[Connector] = None,
+    ):
+        """Initialize PostgresEngine."""
+        # Initialize the parent PGEngine
+        super().__init__(key, pool, loop=loop, thread=thread)
+        self._connector = connector
 
     @classmethod
     async def _create(
@@ -130,13 +141,12 @@ async def _create(
                 "both should be specified to use basic user/password "
                 "authentication or neither for IAM DB authentication."
             )
-        if cls._connector is None:
-            cls._connector = Connector(
-                loop=loop,
-                user_agent=USER_AGENT,
-                quota_project=quota_project,
-                refresh_strategy=RefreshStrategy.LAZY,
-            )
+        connector = Connector(
+            loop=loop,
+            user_agent=USER_AGENT,
+            quota_project=quota_project,
+            refresh_strategy=RefreshStrategy.LAZY,
+        )
 
         # if user and password are given, use basic auth
         if user and password:
@@ -156,23 +166,45 @@ async def _create(
 
         # anonymous function to be used for SQLAlchemy 'creator' argument
         async def getconn() -> asyncpg.Connection:
-            conn = await cls._connector.connect_async(  # type: ignore
-                f"{project_id}:{region}:{instance}",
-                "asyncpg",
-                user=db_user,
-                password=password,
-                db=database,
-                enable_iam_auth=enable_iam_auth,
-                ip_type=ip_type,
-            )
-            return conn
+            async def _connect() -> asyncpg.Connection:
+                return await connector.connect_async(  # type: ignore
+                    f"{project_id}:{region}:{instance}",
+                    "asyncpg",
+                    user=db_user,
+                    password=password,
+                    db=database,
+                    enable_iam_auth=enable_iam_auth,
+                    ip_type=ip_type,
+                )
+
+            # Jump to the background loop to execute connector logic.
+            if loop and asyncio.get_running_loop() != loop:
+                return await asyncio.wrap_future(
+                    asyncio.run_coroutine_threadsafe(_connect(), loop)
+                )
+
+            return await _connect()
 
         engine = create_async_engine(
             "postgresql+asyncpg://",
             async_creator=getconn,
             **engine_args,
         )
-        return cls(PGEngine._PGEngine__create_key, engine, loop, thread)  # type: ignore
+        return cls(PGEngine._PGEngine__create_key, engine, loop, thread, connector=connector)  # type: ignore
+
+    async def _run_as_async(self, coro: Awaitable[T]) -> T:
+        """Run an async coroutine asynchronously."""
+        if not self._loop:
+            return await coro
+        try:
+            if asyncio.get_running_loop() == self._loop:
+                return await coro
+        except RuntimeError:
+            pass
+
+        return await asyncio.wrap_future(
+            asyncio.run_coroutine_threadsafe(coro, self._loop)
+        )
 
     @classmethod
     def __start_background_loop(
@@ -190,7 +222,7 @@ def __start_background_loop(
     ) -> Future:
         # Running a loop in a background thread allows us to support
         # async methods from non-async environments
-        if cls._default_loop is None:
+        if cls._default_loop is None or cls._default_loop.is_closed():
             cls._default_loop = asyncio.new_event_loop()
             cls._default_thread = Thread(
                 target=cls._default_loop.run_forever, daemon=True
@@ -636,3 +668,9 @@ async def _aload_table_schema(
             )
 
         return metadata.tables[f"{schema_name}.{table_name}"]
+
+    async def close(self) -> None:
+        """Close the engine and the connector."""
+        if self._connector:
+            await self._run_as_async(self._connector.close())  # type: ignore
+        await self._run_as_async(super().close())