I think you live in my sister's neighborhood. Their HOA is pretty worthless! Seriously, I would contact an arborist and and get confirmation that your trimming the portion of the tree that is trespassing on your property won't hurt it, then, if it is OK, trim away! First I would send a demand letter requesting that they trim. If they don't then I would sue in small claims court for reimbursement for the arborist and the trimming after you trim and can quantify damages. You might want to have the arborist check out the roots as well.
Actively practicing law in Texas. Inactive licenses in Arizona and Georgia. All answers are general in nature and no attorney/client relationship exists in this forum.
Arizona law does not require that people keep their trees from growing over other peoples' property. Your neighbor is not legally obligated to trim the tree. The HOA might have the power to make them do it, depending on the regulations that are in place. If they will not, then you can trim the part of the tree that overhangs your property yourself, since the neighbor refuses. But you cannot force them to pay for it, since they are not obligated to do it in the first place.