You will probably have to look at an action for private nuisance or trespass against your neighbor and hopefully his/her insurance carrier relating to the property damage the tree has caused. I would suggest you contact a lawyer and proceed to making a claim against that neighbor's carrier. If they do not respond, then you may need to file a lawsuit.
I agree with the previous responder, however, another option is to hire someone to remove the roots from your side of the property line and then sue for that cost. This is if you don't want to wait.
Cheryl P. Baraty