Generally speaking you are allowed to trim the branches of trees that overhang your property but there are conditions, not least that you have to pay for it. Also, if this is strata, you have to establish who owns what.
Here are some other rules, according to City of Sydney Council (but probably apply in most areas):
Rules for Pruning
- Stay on your land: Do not step onto your neighbor’s property to do the work unless they give you direct permission.
- Cut only to the boundary: Stop cutting right at the property line; do not hack away parts of the tree living on your neighbor’s side.
- Do not harm the tree: If your cuts kill or poison the tree, you can be sued for property damage.
- Check local council limits: Some areas protect certain trees or require a permit for heavy pruning if the tree is in a heritage zone or of a protected species.
Also,
- Return the cuttings: Legally, the pruned branches and fruit still belong to the tree owner, so you should offer the offcuts back to your neighbor.