Had this happen TWICE last year, and the neighbor still didn't have a claim even after the second time.
Purchased a 4 plex in Longmont in July. A few days after closing, a big branch broke off a giant elm tree on the corner of our new property and landed on the new neighbor's house as well as her new BMW. Turns out elm is very dense wood, so the extremely heavy branch ripped off a corner of the neighbor's house on its way down: shingles, gutter, soffit, fascia board, even the framing of the overhang lookouts and some of the siding. Also did a ton of damage to the shiny beamer, plus made a mess of the yard. The neighbor (an elderly woman) got my number from our tenants and left me a message. I drove out there ASAP with my chainsaw and trailer, apologized, cleaned it all up really well for her and we traded insurance info. I thought for sure I'd be dealing with a claim, increased rates, possibly getting dropped, etc.
After speaking to my insurance and her insurance I was surprised to find out neither one was planning to cover any of it. Even though it was our tree, the only way we could be held liable was if she had been able to prove negligence on our end. Seeing as we had owned the house only a few days I couldn't be negligent having no history with that tree and not being an arborist. She would have had to have warned me with an official certified letter that the tree was dangerous. I fixed her fence and roof for her because I felt badly about her loss (I had tools and material out there anyway to remodel my building).
I had arborists come out and assess the tree. They removed any dead limbs and advised me to keep it as it was a healthy tree. About a week later, 100mph winds ripped another large portion of the same tree down on the same neighbor's house and driveway AGAIN. This time they had two cars in the driveway, the ill-fated beamer and a nice shiny new Nissan. Both were buried under another giant elm branch, and her grandkids were actually sitting in one of the cars this time (thankfully unharmed). Needless to say she was pissed and vowed to really come after me. Our insurance companies both opened a case. My insurance obtained a letter from my arborist and a copy of the local weather report that recorded 100mph winds. I was cleared of any negligence since I had recently had the tree professionally maintained and it had recently been deemed healthy by a professional. The wind event classified the claim as an Act of God. We were off the hook again. If the neighbor had proper insurance it would probably have covered it, but I don't know how she ended up faring (I haven't brought it up with her, but the beamer is still all cracked up in the driveway a year later so I don't think it was covered).
I had the tree removed after this, $3k. I again removed all the debris from the neighbors property and fixed all the damage to the roof and fence. I just told them, "Let's let the insurance companies figure this out and I'll do what I can to help in the meantime". Since I incurred the cost of removing the tree and fixing their house they knew I had suffered an expense as well, and with the tree being gone now there's nothing else I can do. She apparently didn't have the right insurance coverage so that's on her. I don't see "mature shade trees" as a selling point on listings after this, and I will look up before parking from now on.
In your situation, the lady didn't notify you in the proper way about the tree. The letter, if it did in fact exist, should have been delivered to the owner of the property, not the tenant. If she's a PM she should know the tenant isn't the owner of the tree. She also should have used a certified return letter to verify that you (the owner) received the letter and were notified of the problem. Since there is no official record of the supposed letter, if it goes to court you would just say you never got any notice about the tree and did everything a reasonable person would do to take care of the tree. You had no idea there was a risk of it falling on her car because you are not a tree expert nor clairvoyant and you never received her letter that she gave to the wrong person. If she really wanted to cover her bases she should have documented the dead limbs that posed a risk by taking photos as well as having an arborist inspect the tree and provide her with a letter stating that the tree posed a nuisance or a risk in their professional opinion. Then she should have included both the letter from the arborist and the photos with the certified letter that she sent to you, the owner of the tree. If she doesn't have any of that, she doesn't have much of a case. Also if she knew the tree was such a problem, why then did she choose to park beneath it? Furthermore, it's hard to tell exactly what's going on in that photo, but that tiny little branch looks too small to do any significant damage, and the dents appear to be hail damage (not typical of a tree limb which would be scratches not perfectly round dents). There's a chance her car was actually damaged in the giant hail storm that hit most of Golden last year and now she's looking for a way to repair it using your insurance. If that's the case, insurance experts will be able to determine if the damage to her car is actually hail damage.
If I were you I'd politely extend my deepest sympathy for her car, express relief that no one was injured, thank her for bringing the tree to my attention for the first time, and wish her the best of luck with a potential insurance claim with her car insurance. She'll probably figure out soon enough if she hasn't already that she doesn't have a case against you without a certified letter or any way to prove you were negligent. You probably won't hear from her again.
I'd also remove the tree to avoid any future issues. The tree being gone will provide closure as the risk is no longer there, it's all taken care of, end of story, done. If it happened a 2nd or 3rd time, that would be tricky to explain. Removing the tree shows that you are not the negligent type and would be seen as a positive for you, not an admission of guilt.
