Hello aspirant!!

It is not necessary for you to register your name in the government of tamilndau. You need to get your residential proof and apply for neet. Since you are from other states you may not apply for counseling for the medical college through the government of tamilnadu. You may join into the college  through theanagement seats by securing an eligibility score in neet. If you score a good neet score, you can also opt for all india quota.

For more information about the cmc vellore refer to the following link...

https://www.google.com/amp/s/www.careers360.com/colleges/christian-medical-college-vellore/amp

All the best!!!

Stay safe..