Only !CRM.checkPerm("administer CiviCRM")) conditional works
If you want to use CRM.checkPerm() JS function than you will need to add permission using hook and than it will be catched in CRM.checkPerm() js function. eg: In hook

function extname_civicrm_buildForm($formName, &amp;$form) {
  if ('Some_FormName' == $formName) {
    CRM_Core_Resources::singleton()-&gt;addPermissions('administer CiviCRM');
  }
}


and than in tpl

{literal}
&lt;script&gt;
  CRM.$( function( $ ) {
    if (!CRM.checkPerm("administer CiviCRM")) {
      $( document ).ajaxComplete(function(event, request, settings) {
       //do stuff
      });
    }
  });
{/literal}
&lt;/script&gt;


An other alternate could be

{if !call_user_func(array('CRM_Core_Permission','check'), 'administer CiviCRM')}
  {literal}
  &lt;script&gt;
    CRM.$( function( $ ) {
      $( document ).ajaxComplete(function(event, request, settings) {
        //do stuff
      })
    });
  {/literal}
  &lt;/script&gt;
{/if}