If the tree hangs over the neighbor's property, the neighbor has the right to cut off the overhanging branches. The fact that the tree is no longer as pretty as it was before your neighbor trimmed the branches does not give you any right to sue your neighbor. Your neighbor does not, however, have the right to come onto your property to trim the tree. If you can prove that your neighbor came onto your property, you can sue her for trespass. If your are unsure of your rights, you should consult an experienced real estate lawyer in your area.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.
I agree with Mr. Deason -- any portion of the tree hanging over the property line is fair game to be cut by the neighbor. Roots evading the neighbor's property can also be remove.
Even if the neighbor cut more than allowed, you will have a hard time proving damages. Judges are not eager to put a price tag on leaves and branches.
If the neighbor cut more than allowed and you think it looks bad enough that a judge might give you damages (that a reasonable person would be outraged), then contact a local real estate attorney to review photographs of the tree.
The good thing is the tree will grow back. I have personal experience with the same issue.
This communication is not intended to create an attorney/client relationship. It is always recommended you consult an attorney in person to discuss your case. The Law Offices of Stage & Associates practices state-wide and represents homeowners and community associations. Please visit our website at www.stagelaw.com.