Mere release deed is not sufficient. Society should ask for succession certificate issued by court and on the basis of succession certificate society should transfer the flat. 

the flat and the shares are to be transferred to the releasee's name as mentioned in the release deed

however the society must insist for a legal heirship certificate or a LA to ascertain the actual legal heirs of the deceased owner

for that a petition will have to be filed in the Bombay High Court for grant of an Heirship Certificate or a Letter of Administration 

Only the registered release deed 

did the deceased leave any nominal papers?

you will need his death certificate , indemnity bond to indemnify society in case of third party claims , registered release deed for transfer of flat 

Whether the mutation records of the  property was transferred tot he name of the releasee?

If so, along with the mutation records, death certificate, release deed, if possible NOC from other legal heirs along with the application to transfer the share certificate may be submitted to the society and comply with any other legal requirements including the transfer fee if any.

Release deed, death certificate, legal heir certificate. 

Dear Client,

Release Deed: The registered release deed that has been submitted by the legal heirs is a crucial document. This document establishes the legal transfer of the deceased owner's share in the property to the person mentioned in the release deed.

Death Certificate of the Deceased Owner: This is necessary to establish the death of the original owner.

Probate or Succession Certificate: Depending on the circumstances and the value of the property, a probate or succession certificate is required.

No Objection Certificate (NOC) from Other Legal Heirs: If there are multiple legal heirs mentioned in the release deed, an NOC from other legal heirs might be required, confirming their agreement with the property transfer.

Affidavit by Legal Heirs: Legal heirs are required to submit an affidavit stating their relationship to the deceased owner, their consent to the property transfer.

Indemnity Bond: In some cases, the CHS might require an indemnity bond from the person receiving the property. This bond indemnifies the CHS against any future claims by other legal heirs.

Identity and Address Proof: The person receiving the property might need to provide their identity proof (such as Aadhar card, PAN card, passport, etc.) and address proof.

Passport Size Photographs: Photographs of the person receiving the property are often required for official records.

Payment of Transfer Fees:  CHSs charge a transfer fee for processing ownership transfers.