diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 883201f..cf4d84d 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -3891,6 +3891,37 @@ class TestPostHandshakeAuth(unittest.TestCase):
                 s.write(b'PHA')
                 self.assertIn(b'WRONG_SSL_VERSION', s.recv(1024))
 
+    def test_bpo37428_pha_cert_none(self):
+        # verify that post_handshake_auth does not implicitly enable cert
+        # validation.
+        hostname = 'localhost'
+        client_context = ssl.SSLContext(ssl.PROTOCOL_TLS_CLIENT)
+        client_context.post_handshake_auth = True
+        client_context.load_cert_chain(SIGNED_CERTFILE)
+        # no cert validation and CA on client side
+        client_context.check_hostname = False
+        client_context.verify_mode = ssl.CERT_NONE
+
+        server_context = ssl.SSLContext(ssl.PROTOCOL_TLS_SERVER)
+        server_context.load_cert_chain(SIGNED_CERTFILE)
+        server_context.load_verify_locations(SIGNING_CA)
+        server_context.post_handshake_auth = True
+        server_context.verify_mode = ssl.CERT_REQUIRED
+
+        server = ThreadedEchoServer(context=server_context, chatty=False)
+        with server:
+            with client_context.wrap_socket(socket.socket(),
+                                            server_hostname=hostname) as s:
+                s.connect((HOST, server.port))
+                s.write(b'HASCERT')
+                self.assertEqual(s.recv(1024), b'FALSE\n')
+                s.write(b'PHA')
+                self.assertEqual(s.recv(1024), b'OK\n')
+                s.write(b'HASCERT')
+                self.assertEqual(s.recv(1024), b'TRUE\n')
+                # server cert has not been validated
+                self.assertEqual(s.getpeercert(), {})
+
 
 def test_main(verbose=False):
     if support.verbose:
diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index ec366f0..9bf1cde 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -732,6 +732,26 @@ newPySSLSocket(PySSLContext *sslctx, PySocketSockObject *sock,
 #endif
     SSL_set_mode(self->ssl, mode);
 
+#ifdef TLS1_3_VERSION
+    if (sslctx->post_handshake_auth == 1) {
+        if (socket_type == PY_SSL_SERVER) {
+            /* bpo-37428: OpenSSL does not ignore SSL_VERIFY_POST_HANDSHAKE.
+             * Set SSL_VERIFY_POST_HANDSHAKE flag only for server sockets and
+             * only in combination with SSL_VERIFY_PEER flag. */
+            int mode = SSL_get_verify_mode(self->ssl);
+            if (mode & SSL_VERIFY_PEER) {
+                int (*verify_cb)(int, X509_STORE_CTX *) = NULL;
+                verify_cb = SSL_get_verify_callback(self->ssl);
+                mode |= SSL_VERIFY_POST_HANDSHAKE;
+                SSL_set_verify(self->ssl, mode, verify_cb);
+            }
+        } else {
+            /* client socket */
+            SSL_set_post_handshake_auth(self->ssl, 1);
+        }
+    }
+#endif
+
 #if HAVE_SNI
     if (server_hostname != NULL) {
 /* Don't send SNI for IP addresses. We cannot simply use inet_aton() and
@@ -2765,10 +2785,10 @@ _set_verify_mode(PySSLContext *self, enum py_ssl_cert_requirements n)
                         "invalid value for verify_mode");
         return -1;
     }
-#ifdef TLS1_3_VERSION
-    if (self->post_handshake_auth)
-        mode |= SSL_VERIFY_POST_HANDSHAKE;
-#endif
+
+    /* bpo-37428: newPySSLSocket() sets SSL_VERIFY_POST_HANDSHAKE flag for
+     * server sockets and SSL_set_post_handshake_auth() for client. */
+
     /* keep current verify cb */
     verify_cb = SSL_CTX_get_verify_callback(self->ctx);
     SSL_CTX_set_verify(self->ctx, mode, verify_cb);
@@ -3346,8 +3366,6 @@ get_post_handshake_auth(PySSLContext *self, void *c) {
 #if TLS1_3_VERSION
 static int
 set_post_handshake_auth(PySSLContext *self, PyObject *arg, void *c) {
-    int (*verify_cb)(int, X509_STORE_CTX *) = NULL;
-    int mode = SSL_CTX_get_verify_mode(self->ctx);
     int pha = PyObject_IsTrue(arg);
 
     if (pha == -1) {
@@ -3355,17 +3373,8 @@ set_post_handshake_auth(PySSLContext *self, PyObject *arg, void *c) {
     }
     self->post_handshake_auth = pha;
 
-    /* client-side socket setting, ignored by server-side */
-    SSL_CTX_set_post_handshake_auth(self->ctx, pha);
-
-    /* server-side socket setting, ignored by client-side */
-    verify_cb = SSL_CTX_get_verify_callback(self->ctx);
-    if (pha) {
-        mode |= SSL_VERIFY_POST_HANDSHAKE;
-    } else {
-        mode ^= SSL_VERIFY_POST_HANDSHAKE;
-    }
-    SSL_CTX_set_verify(self->ctx, mode, verify_cb);
+    /* bpo-37428: newPySSLSocket() sets SSL_VERIFY_POST_HANDSHAKE flag for
+     * server sockets and SSL_set_post_handshake_auth() for client. */
 
     return 0;
 }