Yes, it is highly recommended that you give notice to secured creditors and all reasonably ascertainable creditors.  What giving notice does is dramatically reduce the amount of time that creditors have in which to file their claims against the estate.  Any reasonably ascertainable creditor, which includes secured creditors, have two years from the date of death to file claims against the estate, even if the estate publishes a notice to creditors in the newspaper.  This uncertainly can create significant problems in the future if the beneficiaries of the estate have already spent the assets. It could also be a big problem for the personal representative, who released the assets to the beneficiaries without dealing with all the necessary creditor claims.  It is entirely possible that a court would find that a secured creditor was “reasonably ascertainable,” potentially making the personal representative liable for amounts owed to the secured creditor.