This will be the main code
global $current_user, $post;
$user_comment_count = get_comments(array('user_id' => $current_user->ID, 'post_id'=>$post->ID) );
if($user_comment_count) {
the_ratings();
} else {
comment_form(array('class_submit'=>'button'));
}
Also you may want to first check is the user is logged in with the is_user_logged_in()