Yes, you should. It depends on the situation, which type. If they are going to make a decision in the next hour or so, then send an email. If they are going to be making a decision several days or later out, then you can do a handwritten note card.
Do not send through the mail. It makes no sense to post it, send it, and have it returned to the same building. Instead, address it with his or her name and have it sent via internal mail or deliver it to their assistant. You office mail system will help you determine which is best.