neeha I dont think its just for people of tamil nadu... govt cannot discriminate like that... any one who goes to a govt hospital will get treatment. not treating a patient who comes to a govt hospital just because he/she lives in a different place is against the medical ethics.
Soo many ppl from all over the country go to AIIMS, delhi (which again is a govt hospital) for big surgeries.
Nimhans, Bangalore also has patients from all over the country. One transgirl i knew who was living in North east was coming to Nimhans, Bangalore for psychiatric evaluation.
So i doubt that it is only for Tamil people or residents of Tamil Nadu. According to medical ethics they have to treat anyone who goes to them.. But since it is a govt thing they may try to discourage you or make you run pillar to post. But they cant deny you treatment.
Max to max they may ask you for a reference letter from a govt doctor in your residence city forwarding the case to them (stating that they are forwarding ur case to Government Hospital, Chennai due to their lack of surgical expertise of infrastructure ).