A user with the ReplyToTicket right can send Correspondence on a ticket.

This right is granted to the Everyone group in a new RT installation. Under most conditions it is necessary to grant this right to everyone, because otherwise an unprivileged user (e.g. external customer) that accidentally changes E-mail address would not be able to respond to questions on the ticket anymore. Admittedly there are risks associated with this.

Per this post on the rt-users mailing list, it may be best to grant this permission to Requestor instead of Everyone. -- Wohali

See also: Rights, GlobalRights