Approach rta with affidavit of condition of father with medical record seeking transfer and sale of vehicle. On their refusal file a suit in civil for appointment of guardian for sale of property of infirm. Add tra as a party Court will issue appropriate direction  rta for transfer/sale of vehicle. If this is additional question  to earlier question  you can add his immovable properties also in the petition for appointment of guardian as advised earlier.  

You need court orders appointing mother as legal guardian of husband with permission to sell his car 

Dear Sir

You will need to be appointed as your father's legal guardian, then you will have the right to sell his car.

Thank you

- Legally you cannot become the owner of that car without getting the consent of your dad even he is under observation. 

- However, you can move an application before the RTO for taking your dads signature in the presence of the officials of RTO.

- If , he is in coma , then you can approach the court for getting permission for the same. 

You need court permission to do so. You can't do it without it in his this conditions

Neither your father can sell the car nor anyone of you can sell the car while the car is on his name and his condition is that he is in an unstable mental condition/coma.

For selling his property, whether car  or any other immovable property you may have to obtain permission from court 

It is a lengthy procedure to obtain court's permission, i.e., you may have to first get him declared as mentally unfit by the court by producing all medical documents and then seek court to appoint a court guardian to take care of his property including selling them to take care of his medical expenses.

Dear Sir,

You may take medical certificate from the concerned and then take family genealogy and NOC from your mother and other siblings having no objection to sell the car. If prospective buyers are ready then you can sell the vehicle.