Within thirty days after letters are granted on the estate of a deceased member of any partnership, the surviving partner or partners shall file a verified inventory of the partnership in the probate division in which letters are issued on the estate, to be a part of the court records of the administration of the decedent‘s estate. If no letters are issued on the decedent’s estate in this state the surviving partners shall file the inventory within sixty days after the death of a partner in the probate division of the circuit court of the county of which the decedent was a resident at the time of his death or, if a nonresident, in the probate division of the circuit court of the county in which the partnership had its principal business office in this state, the inventory to be indexed under the name of the deceased partner and also the name of the partnership and to be a part of the court records of the administration of the partnership. The inventory shall state the proportionate share of the deceased partner, the aggregate value of the assets of the partnership and the aggregate of its liabilities, but no detailed list of assets or liabilities is required unless ordered by the court. Upon the verified petition of any interested party or on its own motion the court, in its discretion, may order the surviving partners to file a detailed list of assets and liabilities of the partnership and it also may order that the assets of the partnership be appraised as provided by law for the appraisal of the assets of a decedent. On the request of any surviving partner, the court may issue a certificate reciting that he has filed an inventory of the assets of the partnership in accordance with this section and that he will be held to account to the executor or administrator of the estate of the decedent in accordance with the Uniform Partnership Law.