What I found actually surprised me, but in hindsight, perhaps I shouldn't have been so surprised. I'd never noticed the spelling centimeter before, but that's not unusual. Often we don't notice things even thought they are there.
It turned out the American spelling of the distance related words, metre, centimetre, millimetre are meter, centimeter and millimeter respectively. That was a surprise. However in hindsight, given the American spelling of centre is center, where the re is er, it makes sense this spelling may apply to other words, as it does in this case.
The spelling in Australia is thus centimetre.