Given the disagreement amongst the residents regarding pruning of the tree.. and by the sounds of it, reducing the height of the trees, the Body Corporate will need to put forward and pass a motion, to decide what action to take, if they do not already have a motion passed regarding maintenance and pruning of the tree, that permits the planned height change of the trees.
I assume there are no vegetation protection orders covering the trees?
If the tree is on the common property.. then the body corporate are the "tree-keepers", as defined by the Neighbourhood Disputes (Dividing Fences and Trees) Act 2011 (the Act).
Responsibilities of a ‘tree-keeper’
A tree-keeper is responsible for:
• cutting and removing any branches of the tree which overhang a neighbour’s land, provided there is no vegetation protection order protecting the tree
• ensuring that a tree does not:
– cause serious injury to a person on the neighbour’s land
– serious damage to a neighbour’s property
– unreasonably interfere with a person’s use and enjoyment of their land.