I know that in our townhouse complex, trees that are in private courtyards, not accessible to anyone else nor seen by anyone else that with trees, the OC is responsible for the airspace above the courtyards therefore is responsible for the part of any tree in the airspace (I think about 3 metres above the ground). This is for the purpose of pruning/removing or trimming trees, overhanging branches etc.
Here we have paid for the removal or tree branches over hanging another courtyard/roof or fence. Any tree that needed removal, costs were split 50/50 with owner and OC (with council approval or course).
General maintenance of a tree in a private garden/courtyard I would think is the responsibility of the owner.