Trees that cross into, or over from neighbouring yards can be a shared love, a tolerated dislike, or a major issue that can severely damage neighbourly relations. It’s good idea for anyone that has issues with a tree on a boundary to contact a qualified Arborist before they discuss it with the other parties involved. This will give you a better understanding of where you stand legally, and the best way to approach the issue with your neighbour.
In the event of a disagreement, coming to a compromise is obviously the best outcome for both parties, but trees can be a polarising issue. A communication breakdown can add another level of complexity to the situation, and at this point engaging an Arborist to meet with both parties is the best way forward.