diff --git a/google/cloud/alloydb/connector/connector.py b/google/cloud/alloydb/connector/connector.py
index 696e5c5c..f7b0822b 100644
--- a/google/cloud/alloydb/connector/connector.py
+++ b/google/cloud/alloydb/connector/connector.py
@@ -305,15 +305,17 @@ def __exit__(
 
     def close(self) -> None:
         """Close Connector by stopping tasks and releasing resources."""
-        close_future = asyncio.run_coroutine_threadsafe(
-            self.close_async(), loop=self._loop
-        )
-        # Will attempt to gracefully shut down tasks for 3s
-        close_future.result(timeout=3)
+        if self._loop.is_running():
+            close_future = asyncio.run_coroutine_threadsafe(
+                self.close_async(), loop=self._loop
+            )
+            # Will attempt to gracefully shut down tasks for 3s
+            close_future.result(timeout=3)
         # if background thread exists for Connector, clean it up
-        if self._thread:
-            # stop event loop running in background thread
-            self._loop.call_soon_threadsafe(self._loop.stop)
+        if self._thread.is_alive():
+            if self._loop.is_running():
+                # stop event loop running in background thread
+                self._loop.call_soon_threadsafe(self._loop.stop)
             # wait for thread to finish closing (i.e. loop to stop)
             self._thread.join()
 
@@ -325,3 +327,7 @@ async def close_async(self) -> None:
         )
         if self._client:
             await self._client.close()
+
+    def __del__(self) -> None:
+        """Close Connector as part of garbage collection"""
+        self.close()
diff --git a/tests/unit/test_connector.py b/tests/unit/test_connector.py
index bf8ebe4d..a0761245 100644
--- a/tests/unit/test_connector.py
+++ b/tests/unit/test_connector.py
@@ -102,3 +102,16 @@ def test_connect_unsupported_driver(credentials: FakeCredentials) -> None:
             exc_info.value.args[0]
             == "Driver 'bad_driver' is not a supported database driver."
         )
+
+
+def test_Connector_close_called_multiple_times(credentials: FakeCredentials) -> None:
+    """Test that Connector.close can be called multiple times."""
+    # open and close Connector object
+    connector = Connector(credentials=credentials)
+    # verify background thread exists
+    assert connector._thread
+    connector.close()
+    # check that connector thread is no longer running
+    assert connector._thread.is_alive() is False
+    # call connector.close a second time
+    connector.close()