How is responible for cutting a tree down when it hang over the property line?

You can cut down the branches that are hanging into your property
The people who the tree is in their property are the ones that are responsible for deciding and having the actual tree cut down.

Cutting the tree down is the responsibility of the property owner where the bulk of the root is. But if any branches are overhanging the property line, they can be trimmed back by the neighbor. However, if the trimming danages the tree the neighbor can be held responsible.