docs/_theme/sphinx_rtd_theme/searchbox.html

<div role="search">
  <form id ="rtd-search-form" class="wy-form" action="{{ pathto('search') }}" method="get">
    <input type="text" name="q" placeholder="Search docs" />
    <input type="hidden" name="check_keywords" value="yes" />
    <input type="hidden" name="area" value="default" />
  </form>
</div>