I have simply copied this file modules/mod_search/tmpl/default.php to this directory templates/ja_fit/local/html/mod_search/default.php and then on default.php file I have added title="tooltip" code below :
<form action="<?php echo JRoute::_('index.php'); ?>" method="post" class="form-inline">
<?php
$output = '<label for="mod-search-searchword' . $module->id . '" class="element-invisible">' . $label . '</label> ';
$output .= '<input name="searchword" id="mod-search-searchword' . $module->id . '" maxlength="' . $maxlength . '" title="tooltip" class="inputbox search-query input-medium" type="search"' . $width;
$output .= ' placeholder="' . $text . '" />';