The simplest answer to this question is that you could be liable. The storm itself is going to be a major factor in determining where the liability lies, but there are also other factors, such as whether you have undertaken proper preventative measures. For example if the tree was not in good health and you have been neglecting trimming it or having it removed, you could be liable but if the storm is serious enough the damage could be classified an act of God.
To give you a better idea of what an act of God may be, hurricanes are a popular example. Because you had no control over the strength or direction of the storm winds, and if the storm has caused serious damage to other property in the area, it may be ruled as a circumstance beyond human control. If your insurance policy does not define what constitutes an act of God, consult your insurance company and have them clear the question up for you. But it is important that you know what to expect, so make your inquiries before a major storm or catastrophe strikes.
The homeowner is expected to take reasonable precautions concerning trees that are on their property. This includes such things as removing dead limbs or branches that overhang a neighbor's property. It also means that tree which are leaning precariously or have died should be removed. Failure to maintain the trees on your property could contribute to other factors and leave you responsible for damage caused, even if it was caused by a storm that would otherwise be classified as an act of God.