diff --git a/pgconn/errors.go b/pgconn/errors.go
index 3c54bbec0..619578298 100644
--- a/pgconn/errors.go
+++ b/pgconn/errors.go
@@ -107,14 +107,15 @@ func (e *parseConfigError) Unwrap() error {
 }
 
 func normalizeTimeoutError(ctx context.Context, err error) error {
-	if err, ok := err.(net.Error); ok && err.Timeout() {
+	var netErr net.Error
+	if errors.As(err, &netErr) && netErr.Timeout() {
 		if ctx.Err() == context.Canceled {
 			// Since the timeout was caused by a context cancellation, the actual error is context.Canceled not the timeout error.
 			return context.Canceled
 		} else if ctx.Err() == context.DeadlineExceeded {
 			return &errTimeout{err: ctx.Err()}
 		} else {
-			return &errTimeout{err: err}
+			return &errTimeout{err: netErr}
 		}
 	}
 	return err
diff --git a/pgconn/pgconn.go b/pgconn/pgconn.go
index 1ccdc4db9..0203cf194 100644
--- a/pgconn/pgconn.go
+++ b/pgconn/pgconn.go
@@ -289,7 +289,7 @@ func connect(ctx context.Context, config *Config, fallbackConfig *FallbackConfig
 		pgConn.contextWatcher.Unwatch() // Always unwatch `netConn` after TLS.
 		if err != nil {
 			netConn.Close()
-			return nil, &connectError{config: config, msg: "tls error", err: err}
+			return nil, &connectError{config: config, msg: "tls error", err: normalizeTimeoutError(ctx, err)}
 		}
 
 		pgConn.conn = nbTLSConn