Catalogsearch form:

Catalogsearch > form.mini.phtml

$category = Mage::getModel('catalog/category');
if (is_object(Mage::registry('current_category'))) {
    $current_category_path = Mage::registry('current_category')->getPathIds();
} else {
    $current_category_path = array();
}
$category->load(Mage::app()->getStore()->getRootCategoryId());
$children_string = $category->getChildren();
$children = explode(',', $children_string);
$extra_options = '';
foreach ($children as $c) {
    $selected = (in_array($c, $current_category_path)) ? 'SELECTED' : '';
    $extra_options.= '<option value="' . $c . '" ' . $selected . '>' . $category->load($c)->getName() . '</option>' . "\n";
}
?>
 
<form id="search_mini_form" action="<?php echo $this->helper('catalogSearch')->getResultUrl() ?>" method="get">
    <fieldset>
        <legend><?php echo $this->__('Search Site') ?></legend>
        <span style="float: left; position: relative; top: 8px; left: 15px;">Search</span>
        <div class="mini-search">
            <select name="cat" id="cat" class="input-text">
                <option value="">All Products</option>
                <?= $extra_options ?>
            </select>
            <input id="search" type="text" class="input-text" name="<?php echo $this->helper('catalogSearch')->getQueryParamName() ?>" value="<?php echo $this->helper('catalogSearch')->getEscapedQueryText() ?>"  placeholder="<?php echo $this->quoteEscape($this->__('Search entire store here...')) ?>" />
            <button type="submit" title="<?php echo $this->quoteEscape($this->__('Search')) ?>" class="button search-button" value="Go"><span><span><?php echo $this->__('Search') ?></span></span></button>
            <div id="search_autocomplete" class="search-autocomplete"></div>
            <script type="text/javascript">
                //<![CDATA[
                var searchForm = new Varien.searchForm('search_mini_form', 'search', '<?php echo $this->__('Search your products') ?>');
                searchForm.initAutocomplete('<?php echo $this->helper('catalogSearch')->getSuggestUrl() ?>', 'search_autocomplete');
                //]]>
            </script>
        </div>
    </fieldset>
</form>