you should set name attribute of your column and add some logic in search method of model
example:
in model class do something like following
public $registered;
//remember to add this new attribute to your search rule
public function rule()
{
return array(
//other rules
array('registered','safe', 'on'=>'search'),
);
}
public function search()
{
$criteria=new CDbCriteria;
if($this->registered=='no')
$criteria->addCondition('password is null');
elseif($this->registered=='yes')
$criteria->addCondition('password is not null');
//your other search criteria
return new CActiveDataProvider($this, array(
'criteria'=>$criteria,
));
}