Permission base on the administration menu?
I found the solution here is how is done....

function my_custom_module_page_build(&amp;$page) {

    // Check if user have access to the administration menu
    if (!user_access('access administration menu')) return false;

    // Check if user have access to navbar.
    if (!user_access('access navbar')) return false;

     drupal_add_css(drupal_get_path('module', 'my_custom_module') . '/css/mobile.css');

}