Maybe the easiest way to explain this is to tell the proper way to do it.

Contrary to what Shelly said, the issue is to have everything on the same ground (earth).

If two things are grounded to the same thing they don't pass electricity between them, they both pass it to the ground. The real way to do this is to have your wrist strap that plugs into your static pad which plugs into your ground.

If you are plugged into the wall and the computer is plugged into the wall, you are both on the same ground (earth).

If you are not plugged into the wall but your computer is, you are not on the same ground. Touching the case puts you on the same circuit as your computer ground. You to case to ground, mobo to case to ground.

Likewise, if you are plugged into the wall but the computer is not, you are not on the same ground. And likewise, touching the case puts you both on the same circuit. You to ground, mobo to case to you to ground.

When you and the case are on the same ground no electricity will pass between you and the motherboard.

If you don't have a strap and the computer is plugged into a ground, periodically touch the case to relieve any static that you may build up while moving around.

So wear your wrist strap and touch the case before messing around in it. Since the computer is not moving around you won't have to worry much about it building up static. You are the most important item to keep grounded because you are the one most likely to build up a discharge.

(edit)I forgot one other option which serlv covered below. Neither you or the computer is grounded to earth. You touch the case and the ground circuit is, you to case, mobo to case. Using that method I would stay in constant contact with the case because no electricity build up is going away, it's just not passing between you and the motherboard.(/edit)