That seems like a custom adsense search something you would add near your navbar template
<style type="text/css">
@import url(http://www.google.com/cse/api/branding.css);
</style>
<div class="cse-branding-right" style="background-color:#FFFFFF;color:#000000">
<div class="cse-branding-form">
<form action="http://www.google.com/cse" id="cse-search-box" target="_blank">
<div>
<input type="hidden" name="cx" value="partner-pub-1699245511152881:s9hu62t33yo" />
<input type="hidden" name="ie" value="ISO-8859-1" />
<input type="text" name="q" size="30" />
<input type="submit" name="sa" value="Search" />
</div>
</form>
</div>
<div class="cse-branding-logo">
<img src="http://www.google.com/images/poweredby_transparent/poweredby_FFFFFF.gif" alt="Google" />
</div>
<div class="cse-branding-text">
Custom Search
</div>
</div>