diff --git a/Lib/asyncio/sslproto.py b/Lib/asyncio/sslproto.py
index ab7ff0b..6e9ce29 100644
--- a/Lib/asyncio/sslproto.py
+++ b/Lib/asyncio/sslproto.py
@@ -551,8 +551,11 @@
     def _start_shutdown(self):
         if self._in_shutdown:
             return
-        self._in_shutdown = True
-        self._write_appdata(b'')
+        if self._in_handshake:
+            self._abort()
+        else:
+            self._in_shutdown = True
+            self._write_appdata(b'')
 
     def _write_appdata(self, data):
         self._write_backlog.append((data, 0))