Taken from my Reports MOD article:
This will still make the ticket show up under "My Tickets" (even when closed) in order to get it to stop doing that (if you desire), then change the following entry
from:
include/staff/tickets.inc.php
$qwhere.=' AND ticket.staff_id='.db_input($staffId);
to:
$qwhere.=' AND ticket.status="open" AND ticket.staff_id='.db_input($staffId);