diff --git a/tests/protocols/test_websocket.py b/tests/protocols/test_websocket.py
index 8971a7d97..e7285449c 100644
--- a/tests/protocols/test_websocket.py
+++ b/tests/protocols/test_websocket.py
@@ -7,6 +7,8 @@
 import httpx
 import pytest
 import websockets
+import websockets.asyncio
+import websockets.asyncio.client
 import websockets.client
 import websockets.exceptions
 from typing_extensions import TypedDict
@@ -603,18 +605,15 @@ async def app(scope: Scope, receive: ASGIReceiveCallable, send: ASGISendCallable
 
     async def websocket_session(uri: str):
         async with httpx.AsyncClient() as client:
-            try:
-                await client.get(
-                    f"http://127.0.0.1:{unused_tcp_port}",
-                    headers={
-                        "upgrade": "websocket",
-                        "connection": "upgrade",
-                        "sec-websocket-version": "13",
-                        "sec-websocket-key": "dGhlIHNhbXBsZSBub25jZQ==",
-                    },
-                )
-            except httpx.RemoteProtocolError:
-                pass  # pragma: no cover
+            await client.get(
+                f"http://127.0.0.1:{unused_tcp_port}",
+                headers={
+                    "upgrade": "websocket",
+                    "connection": "upgrade",
+                    "sec-websocket-version": "13",
+                    "sec-websocket-key": "dGhlIHNhbXBsZSBub25jZQ==",
+                },
+            )
 
     config = Config(app=app, ws=ws_protocol_cls, http=http_protocol_cls, lifespan="off", port=unused_tcp_port)
     async with run_server(config):
diff --git a/uvicorn/protocols/websockets/websockets_sansio_impl.py b/uvicorn/protocols/websockets/websockets_sansio_impl.py
index ea70236b2..994af07e7 100644
--- a/uvicorn/protocols/websockets/websockets_sansio_impl.py
+++ b/uvicorn/protocols/websockets/websockets_sansio_impl.py
@@ -119,17 +119,14 @@ def eof_received(self) -> None:
         pass
 
     def shutdown(self) -> None:
-        if not self.transport.is_closing():
-            if self.handshake_complete:
-                self.queue.put_nowait({"type": "websocket.disconnect", "code": 1012})
-                self.close_sent = True
-                self.conn.send_close(1012)
-                output = self.conn.data_to_send()
-                self.transport.write(b"".join(output))
-            elif not self.handshake_initiated:
-                self.send_500_response()
-                self.queue.put_nowait({"type": "websocket.disconnect", "code": 1006})
-            self.transport.close()
+        if self.handshake_complete:
+            self.queue.put_nowait({"type": "websocket.disconnect", "code": 1012})
+            self.conn.send_close(1012)
+            output = self.conn.data_to_send()
+            self.transport.write(b"".join(output))
+        else:
+            self.send_500_response()
+        self.transport.close()
 
     def data_received(self, data: bytes) -> None:
         self.conn.receive_data(data)
@@ -161,7 +158,6 @@ def handle_connect(self, event: Request) -> None:
         self.request = event
         self.response = self.conn.accept(event)
         self.handshake_initiated = True
-        # if status_code is not 101 return response
         if self.response.status_code != 101:
             self.handshake_complete = True
             self.close_sent = True