Share certificate holder is dead

Obtain the death certificate and Legal Heir certificate from the concerned and request the committee of the society to transfer in their name.  Transfer fee may be levied.

The legal heirs of the deceased flat owner are entitled to inherit/succeed to the estates of the deceased  if he is reported to have died intestate.

The succession law is applicable for acquiring share certificate also.

Hence as advised you obtain a legal heirship certificate and along with the a copy of the death certificate submit the applicaiton for transfer of share certificate to your names jointly 

Have you enquired with the Office-beares of the Society?

What is this one document? What is the constraint in executing this document before the Notary

If you have given an affidavit about the legal heirs then you are required to get it attested.

If the legal heirship has been obtained from the government revenue department then you don't have to get it notarized because that is a substantial document to establish your legal heirship status.