Who is financially responsible for trimming neighbors overhanging trees into our backyard?

Whomever desires to have the overhanging branches trimmed would be financially responsible. Note that in California, you do not have the absolute right to cut or remove branches from your neighbor's tree. In the case of Booska v. Patel (1994) 24 Cal. App. 4th 1786, the California Court of Appeal held that a neighbor does not have the absolute right to cut encroaching roots and branches so that they end at his or her property line. You must take into account the health of the tree before you start trimming, cutting or chopping. You might be liable for reasonable costs of replacing destroyed tree with identical or substantially similar tree. Therefore, you ought to communicate with your neighbor before you take any action. Perhaps you can come to an agreement with your neighbor regarding sharing this cost?