You can remove the search by editing the header.tpl file in template folder.

Findout the following code and remove it
HTML Code:
    <div id="video-search">
       <form method="get" action="{$base_url}/search.php">
         <input class="text" value="{$smarty.request.search}" name="search" />
         <input type="hidden" name="type" value="video">
         <input type="submit" class="search-btn" value="Search" />
       </form>
    </div>