Do you have municipal by-law enforcement officers? Here, we have by-laws that govern such things and it is up to that department of the city to interpret, administer and enforce such things. Where I live, it is the owner of the tree to bear the expense of ensuring that his tree doesn't enfringe upon another person's property when it is against the wishes of that person.
My neighbour has very tall trees also that overhang my house and yard. It can sometimes be construed as a hazard (falling branches). The branches, if they touch my roof or house, would be responsible to shortening the lifespan of my shingles and siding. It is up to my neighbour to hire a "tree guy" to prune it back. I get along very well with my neighbour and would never have such a problem as you do. In the same token, she take the initiative to hire the pruner long before this becomes an issue.
You should look into your municipal government to see if such a department exists. If it does and there is a law governing such things, they will issue a summons to your neighbour to get the work done.