You need to review your and see what it says about the sinkhole testing. Also ask your insurance company for a letter explaining why they will not pay for the testing. They usually do not like to put things in writing.
If there is a sinkhole next door you may need to start looking for a new place to live.
DISCLAIMER: David J. McCormick is licensed to practice law in the State of Wisconsin and this answer is being provided for informational purposes only because the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship.
Your insurance company likely isn't necessarily telling you the whole truth about sinkhole testing because they want to avoid the cost of testing. Contact our office for a free case consultation to discuss your rights as a homeowner with a potential sinkhole. The law change has made it more difficult in some ways to make claims but many insurance company's are interpreting the statute in a manner wholly inconsistent with the intent of the statute to preclude folks like you from receiving the benefit of testing.
This answer does not, nor is it intended to, create an attorney-client relationship or constitute attorney advertising. Rather, it is offered solely for informational purposes. The facts of each case are different and unique, it is critical to consult with qualified counsel with whom information can be shared and assessed under attorney-client privilege, so that competent and quality advice can be obtained on which you can make informed decisions