On notice of what? "On notice about the tree"? I'm pretty sure they OP knew the tree was there before the neighbor pointed it out.The neighbor is now on notice about the tree.
The original post tells us that the OP's neighbor "sent [the OP] a letter . . . to get it removed stating his concerns that if the tree falls it can lead to a dangerous situation such as property damage, auto damage or injury." In other words, the only thing that the OP's neighbor has put the OP on notice of is an unsubstantiated concern about some hypothetical possibility that is true of every tree. According to what the OP told us, the neighbor has not articulated any facts that would support a conclusion that the tree is anything but perfectly healthy. Putting someone on notice that you have a vague and unsubstantiated concern is not legally meaningful.