Who is legally responsible for removing the fallen tree section?

A tree adjacent to the property line between property A and property B breaks in half, some 20 feet above ground, during a rain storm. The tree appears to be growing out of the property of B, but the tree trunk and branch segments which have broken (but still attached to the main trunk by tree shards) normally hung over the property line to shade property A. The broken section now lies on property A, and is still partially attached to the main trunk by the aforementioned wood shards.Who pays for removal and cleanup?