The drop down would have to trigger an Javascript action that would pass the approved / denied request to the server. Be it ajax, or simply an href or form submit, that would depend on how you want to record whether the comment was approved or denied
Lets say for instance the drop down is in a form tag with action to comment_changestatus.php
inside of the form element would be your <select> tag with a javascript trigger. perhaps a hidden varaible to keep which commetn you are approving/denying
like so:
<form action="comment_changestatus.php" name="myformID" method="post" name="mycomment">
<select name="commentID" onChange='document.myformID.submit()'>
<option value='0'>Deny</option>
<option value='1'>Approve</option>
</select><input type="hidden" name="comment" value="COMMENT_ID">
</form>
and then on the PHP page, or even just a PHP_SELF page, you would update the comment accordingly