For a mere overhang you may act yourself under sec. 422 ABGB but bear the costs yourself.
Where roots of a neighbour’s tree reach into your soil or branches reach into your airspace, you may remove or cut them off yourself under sec. 422 ABGB and may also use the branches cut off. A prior request to the neighbour is not necessary for this. The only condition is that you proceed professionally and spare the plant as far as possible.
If there is no damage and none is threatening, you bear the costs of removal yourself. If you proceed improperly and harm the tree, you may make yourself liable to compensate the neighbour. In case of doubt, a legal assessment clarifies the right path.