The city building inspector, or maybe the city PA could at least tell you what your rights are in regards to trimming the tree back to the property line, if not go to city hall and ask the clerk who could explain your rights in this matter, someone there has to know.
Are there any power lines close by, if so the power company has the right to trim the tree back if it puts the power line in danger.
As stated above anything crossing the property line should be your right to trim it back, if you can't get a clear answer from city hall, perhaps consult an attorney, it shouldn't cost that much just to get a clear answer about your rights on this issue.
Oh another idea, perhaps check with the county, and state, at some level there has to be some kind of law covering this matter, basically his tree is encroaching on your property.
There could very well be a law that certain structures and things like trees must be X number of feet from the property line.
I know in our area, anything crossing a property line I have the right to take whatever action I deem proper to correct the problem, a property line is not something drawn on the ground only, it extends upward to include the airspace above the property.
If he is not willing to trim the tree then ask him if he would rather do it "Before" you take him to court and not only get a court order to either trim it or cut it down completely, (If I have to take this to court I will be pushing to have the tree completely removed or seriously cut back and topped so it no longer presents a danger to my property should it come down during a storm or something), plus damages resulting from the tree shedding leaves and debris in you pool and property that you have to constantly clean up, in civil court you are allowed to sue for damages + Labor, (at the going rate for landscapers) + court costs.
If you do have to take him to court, just explain the clear and present danger to "ALL" of your property and persons, plus the "LITTER" the tree is causing, and the time and effort required on your part to clean it up, plus the additional cost involved with cleaning and maintaining your pool.
One last idea would to perhaps contact your insurance agent and point out the issue to him and see if your insurance company might be willing to get involved to reduce their exposure should the tree fall or a big branch break off.
Well that is about all I can think of right now.
Hope something I have said will help, and if not I hope all the best for you getting the situation resolved to your satisfaction.