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I am sorry to hear about this situation. Provided that the tree did not fall due to an Act of God (such as a hurricane) - but even if it did the neighbor can be liable if she did not properly tie down the tree prior to the event - then the neighbor is liable. It is a very clear cut case - if the neighbor's tree damages one's property, then one can pursue the neighbor for the damage in such situations.
The suit may be brought before or after fixing the damage one's self. If brought before, estimates can be used to argue what amount should be granted in judgment. If brought after, actual bills can be used as proof of the damage amount in asking for judgment.
NOTE that the Plaintiff (i.e. you) is expected to mitigate damages. This means that if you have a way to minimize the financial damage (such as using one's insurance to partially cover the costs), this is expected.
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