this post can not be answered based on the insufficiency of details. If the "petition" is a document that was submitted as part of a governmental or legal procedure pertaining to the issuance of permit(s), it may be difficult to be used as a basis for a defamation action, even if there are errors of fact in the contents. On the other hand, if the petition was filed, and a governmental agency conducted an investigation, thereafter denying your permit based on a confirmation of the complaining petition, you might have a problem as it gives their petition a "color of truth" and truth is a defense to a claim of defamation. If the petiition is based on opinions about how your business/building will adversely affect the neighborhood, again you have problems with pursuing a defamation action. Get a sit down consult iwth an attorney where you can go over the details in private.