You need to give an application to the society informing them about death of your father alongwith death certificate copy and ask them to the transfer the flat to your mother as her name is there in the nomination form.
With regards to withdrawal of your name, you need to give a relinquishment deed in favour of your mother, copy of that deed needs to be given to the society.
The society will give you a transfer form, which needs to be duly filled up alongwith notarized documents.
If your mother and you are the only legal heirs, then it is advisable to have the property jointly in the name of your mother and yours as it would save future hardships, in transfering the flat in your name.
For furhter clarrification, you may call on 9324538481.
Adv. Rohit Dalmia