diff --git a/tests/client.rs b/tests/client.rs
index 43e1f08acb..80e77d589c 100644
--- a/tests/client.rs
+++ b/tests/client.rs
@@ -21,6 +21,7 @@ use futures_channel::oneshot;
 use futures_util::future::{self, FutureExt, TryFuture, TryFutureExt};
 use support::TokioIo;
 use tokio::net::TcpStream;
+
 mod support;
 
 fn s(buf: &[u8]) -> &str {
@@ -2009,6 +2010,74 @@ mod conn {
             .expect_err("client should be closed");
     }
 
+    #[tokio::test]
+    async fn http2_connect_detect_close() {
+        // Regression test for failure to fully close connections when using HTTP2 CONNECT
+        // We send a request, read/write some data, then drop the client connection.
+        use futures_util::future;
+        let (listener, addr) = setup_tk_test_server().await;
+        let (tx, rx) = oneshot::channel::<()>();
+        const BODY: &[u8] = b"hello world";
+        tokio::task::spawn(async move {
+            use hyper::server::conn::http2;
+            use hyper::service::service_fn;
+
+            let res = listener.accept().await;
+            let (stream, _) = res.unwrap();
+            let stream = TokioIo::new(stream);
+
+            let service = service_fn(|req: Request<hyper::body::Incoming>| {
+                tokio::task::spawn(async move {
+                    let io = &mut TokioIo::new(hyper::upgrade::on(req).await.unwrap());
+                    let mut buf: [u8; BODY.len()] = [0; BODY.len()];
+                    io.read_exact(&mut buf).await.unwrap();
+                    io.write_all(BODY).await.unwrap();
+                });
+
+                future::ok::<_, hyper::Error>(Response::new(Empty::<Bytes>::new()))
+            });
+
+            tokio::task::spawn(async move {
+                let conn = http2::Builder::new(TokioExecutor).serve_connection(stream, service);
+                conn.await.unwrap();
+                drop(tx);
+            });
+        });
+
+        let io = tcp_connect(&addr).await.expect("tcp connect");
+        let (mut client, conn) = conn::http2::Builder::new(TokioExecutor)
+            .handshake(io)
+            .await
+            .expect("http handshake");
+
+        tokio::task::spawn(async move {
+            conn.await.expect("client conn");
+        });
+
+        // Sanity check that client is ready
+        future::poll_fn(|ctx| client.poll_ready(ctx))
+            .await
+            .expect("client poll ready sanity");
+
+        let req = Request::builder()
+            .method(Method::CONNECT)
+            .uri(format!("{}", addr))
+            .body(Empty::<Bytes>::new())
+            .expect("request builder");
+
+        let resp = client.send_request(req).await.expect("req1 send");
+        assert_eq!(resp.status(), 200);
+        let io = &mut TokioIo::new(hyper::upgrade::on(resp).await.unwrap());
+
+        let mut buf: [u8; BODY.len()] = [0; BODY.len()];
+        io.write_all(BODY).await.unwrap();
+        io.read_exact(&mut buf).await.unwrap();
+        drop(client);
+        let _ = tokio::time::timeout(Duration::from_secs(1), rx)
+            .await
+            .unwrap();
+    }
+
     #[tokio::test]
     async fn http2_keep_alive_detects_unresponsive_server() {
         let (listener, addr) = setup_tk_test_server().await;