Investor13, if you do a search on this site for trees there are a couple of informative posts on this issue. In particular one by mattb on 14/3/13 and another by struggler on 25/3/12.
The view appears to be that if a tree is higher than a certain height (2 or 3m) it is OC responsibility but if smaller than that it is the owners.
There is also the memorandum by the land and property office on this called “Defining who is responsible for items and areas in a Strata Scheme”. Section 2.5 and 2.6 say something about tree responsibility. I don’t have the exact link for the memorandum but am sure a google search will help you find.