How do I go about filing a Petition to Dismiss Probate case?

If an Inventory & Appraisal hasn't been filed, you can file a Judicial Counsel Form CIV-110 "Request for Dismissal". If an Inventory & Appraisal has been filed, you will need to prepare a "Petition Requesting Dismissal of Probate and Discharge of Personal Representative" and ask the Judge for permission to dismiss the case. That is not a preprinted "form" document. This information is not intended to substitute for professional legal advice and does not create an attorney-client relationship. You should accept legal advice only from a licensed legal professional with whom you have an attorney-client relationship.