How to limit users to one comment per post

I am using WordPress as a petition site and hacking the comments system to work as the petition signup. I would like to find out how I can limit a user to post only one comment per post. So far I can limit each user to one comment on the whole WordPress site as shown in the code below, but that’s not what I am looking to accomplish.

Again, how can I limit each user to one comment per post?

   <?php
   /*
    * Single Petition Template
    * @package WordPress
    * @subpackage Twenty_Thirteen
    * @since Twenty Thirteen 1.0
    * template author: Facinet Toure
    * website URL: http://mongage.com
   */

 get_header(); ?>

 <div id="primary" class="content-area">
  <div id="content" class="site-content" role="main">
    <?php /* The loop */ ?>
    <?php while ( have_posts() ) : the_post(); ?>
    <?php //get_template_part( 'content', get_post_format() ); ?>
    <!-- post format -->
    <article id="post-<?php the_ID(); ?>" <?php post_class(); ?>>
        <header class="entry-header">
            <?php if ( has_post_thumbnail() && ! post_password_required() ) : ?>
            <div class="entry-thumbnail">
                <?php the_post_thumbnail('full'); ?>
            </div>
            <?php endif; ?>
            <h1 class="entry-title">
                <?php the_title(); ?>
            </h1>
            <p><span class="rounded-corners alignleft"><?php echo get_avatar( $post->post_author, 74 ) ?></span>
                <span class="author"><?php the_author_meta( 'display_name' ); ?></span>
                <span> | </span>This post currently has
                <?php comments_number( 'no responses', 'one response', '% responses' ); ?>
                .</p>
        </header>
        <!-- .entry-header -->
        <div class="entry-content">
            <?php the_content( __( 'Continue reading <span class="meta-nav">&rarr;</span>', 'twentythirteen' ) ); ?>
            <?php wp_link_pages( array( 'before' => '<div class="page-links"><span class="page-links-title">' . __( 'Pages:', 'twentythirteen' ) . '</span>', 'after' => '</div>', 'link_before' => '<span>', 'link_after' => '</span>' ) ); ?>
        </div>
        <!-- .entry-content -->

        <footer class="entry-meta">
            <?php twentythirteen_entry_meta(); ?>
            <?php if ( comments_open() && ! is_single() ) : ?>
            <span class="comments-link">
            <?php comments_popup_link( '<span class="leave-reply">' . __( 'Sign the petition', 'twentythirteen' ) . '</span>', __( 'One comment so far', 'twentythirteen' ), __( 'View all % comments', 'twentythirteen' ) ); ?>
            </span><!-- .comments-link -->
            <?php endif; // comments_open() ?>
            <?php edit_post_link( __( 'Edit', 'twentythirteen' ), '<span class="edit-link">', '</span>' ); ?>
            <?php if ( is_single() && get_the_author_meta( 'description' ) && is_multi_author() ) : ?>
            <?php get_template_part( 'author-bio' ); ?>
            <?php endif; ?>
        </footer>
        <!-- .entry-meta --> 
    </article>
    <!-- #post -->

    <p> This post currently has
        <?php comments_number( 'no responses', 'one response', '% responses' ); ?>
        . </p>
    <?php twentythirteen_post_nav(); ?>
    <ol reversed class="commentlist">
        <?php
    //Gather comments for a specific page/post 
    $comments = get_comments(array(
        'post_id' => $post->ID,
        'status' => 'approve' //Change this to the type of comments to be displayed
    ));

    //Display the list of comments
    wp_list_comments(array(
        'per_page' => -1, //Allow comment pagination
        'reverse_top_level' => false, //Show the latest comments at the top of the list,
        'max_depth' => '1',
        'avatar_size' => 0,
    ), $comments);
?>
    </ol>
    <?php // check if user has previously commented the post
        global $current_user;
        if ( !is_user_logged_in() ) {
        echo 'you must be logged in to sign the petition';
        } else {
        $args = array('user_id' => $current_user->ID);
        $usercomment = get_comments($args);
        if(count($usercomment) >= 1) { 
            echo '<p>Vous avez déjà signé cette pétition. S'il vous plaît partager avec votre famille et vos amis</p>';

        } else { comment_form(); 
        } 
    }?>
    <?php endwhile; ?>
   </div>
   <!-- #content --> 
   </div>
  <!-- #primary -->

<?php get_sidebar(); ?>
<?php get_footer(); ?>