Custom search box in magento on homepage

//.phtml file

<?php echo $this->getLayout()->createBlock('core/template')->setTemplate('catalogsearch/form.mini.phtml')->toHtml(); ?>

// in CMS page

{{block type="core/template" name="top-search" as="top-search" template="catalogsearch/form.mini.phtml"}}

//customize search box as per you need

path         =   app/design/frontend/rwd/tt/template/catalogsearch/

filename  =    form.mini.phtml file