Driving around town this past week, I've seen a huge number of Montclair homes that were hit hard by the snowstorm of October 29. Drooping power lines and downed trees are unfortunately a common sight these days. Power lines are obviously a matter for PSE&G to deal with; trees, however, may be your responsibility.
If one of your trees falls on your own property, it is your responsibility to get it to the curb; the town of Montclair will then remove it for you. Any damage to your home is also your responsibility--call your insurance company.
But what if a neighbor's tree falls on your property? In an article on the website Houselogic.com, DC-area author Ann Cochran explains that you should still contact your own insurance company. The cost of removing it is your neighbor's responsibility only if you can prove that he knew that the tree was at risk of falling (due to disease, e.g.) and did nothing about it. In the case of a freak snowstorm, this is unlikely.
The same logic applies if one of your trees falls onto your neighbor's property. Cochran recommends doing nothing until you hear from your neighbor's insurance company. Removing the tree is your responsibility only if your neighbor can prove that you knew it was a hazard and did nothing about it. Having said that, it's always neighborly to offer to remove the branches - even if legally, it's not your responsibility.
Property damage is very upsetting. Knowing your rights and responsibilities as a homeowner is a good way to prevent it from escalating into a neighborhood dispute.