How hidden the user_filter_form to a specific role?
hook_form_alter() wouldn't actually be the best place for this; the form is actually called in from user_admin() so the best place for your code would be hook_page_alter().

The first thing you should do is create a custom permission that you can assign to the role:

function MYMODULE_permission() {
  return array(
    'access user filter form' =&gt;  array(
      'title' =&gt; t('Access User Filter Form')
    ),
  );
}


Then implement hook_page_alter() to hide the form:

function MYMODULE_page_alter(&amp;$page) {
  // Make sure this is the right page
  if (arg(0) == 'admin' &amp;&amp; arg(1) == 'people') {
    // Make sure filter form actually exists
    if (isset($page['content']['system_main']['user_filter_form'])) {
      // Check user access
      if (!user_access('access user filter form')) {
        // Deny access to the form if necessary
        $page['content']['system_main']['user_filter_form']['#access'] = FALSE;
      }
    }
  }
}