Hello,
As you know admission to government medical colleges is based on NEET marks is done under two categories-All India quota(15%) and state quota(85%).
The state quota is only available to students having domicile of that state and not for outsiders. Since you belong to Bihar , you are not eligible to get state quota seats in Tamil Nadu. However if you have high enough marks you can go fo All India Quota seats in Tamil Nadu.
Counselling process for most of the states has started.
To know more follow this link-
https://www.google.com/amp/s/medicine.careers360.com/articles/neet-counselling/amp
Good luck

Dear Ranjan, Tamilnadu is not an Open State. If you want to apply for Government Medical Colleges of Tamilnadu, you should try under All India Counselling where 15% seats kf Tamilnadu GMCs arr contributed to Central Pool. Now with Round 2 counselling also almost being over at All India  counselling level, you only have a chance in mop up round where Deemed/Central Universities seats are filled. And now your chances are little for Tamilnadu GMCs if you havent applied in earlier rounds.