Here are the rules I have been asked to apply, to the events that I referee:
You may not use any mechanical device. In principle, your
own hand is a mechanical device, so you may not use your
fingers to count liberties.
You may write whatever you like on a sheet of paper, so long
as you explain everything you have written to your opponent
on request. For example, you may write down and add up the
sizes of all the territories.
Nick