That is true. Here is I searched, and I quote

Your Responsibilities

When a tree on your property hangs over the boundary line into another yard, you have a duty to address all weak or damaged branches. If a weak or damaged branch that you failed to remove or maintain falls into the adjoining yard and causes damage to structures, land, people or pets, you are legally responsible. On the other hand, you're not responsible for the tree's debris that falls into the yard next door; that debris includes leaves, acorns, seeds and pods. The neighbor is always responsible for cleanup of the accumulation of those items.