Instead, they wanted me to pay 50% of a bill to have someone cut the branches down. I am neither legally obligated to do so nor do I have the financial resources to do so.
Today they somehow got ahold of my phone number and telephoned. I reiterated what I said. That somehow wasn't good enough for them, so they had the police intervene for "conflict mediation." The officers at first were taking the couple's side, but I was able to have one of them come into my house where I explained my situation and the legal situation. It was clear neither officer knew what the law in this regard was. The cop was trying to talk me into renting a chainsaw and having "a guy come in and cut the branches down." I explained this was utterly ridiculous.
IIRC if I tell the neighbor to "go ahead and cut whatever is on your side," they can legally do so and are absolved from any potential lawsuits on my part. IIRC I am not at all legally responsible for the part of my tree that hangs over onto their property.
The neighbors are now threatening to take me to small claims court over this. I am L-I-V-I-D.