CComment docs

Show captcha only for guests?

If you wish to show the captcha for only unregistered users you'll have to make a small trick. You need to create a Guest group and assign the captcha to this group.

On Joomla! 2.5 the guest group is not existing and you'll have to create it followingthis tutorial.

On Joomla! 3.x the guest group is created during the Joomla! installation so you just have to assign your captcha to this group. (Also make sure that under the Users configuration (users -> groups -> options) "guest user group" is set to guest)