No. You cannot work in another state if you are currently registered with some other state.

For working in another state, you have to be registered in that state, so you have to fill the registration form of that state.

After the submission of the application, the new state will send mail to your original state of registration, to confirm your registration. And a NOC (No Objection Certificate) is issued from your current state of registration.

You can submit the application ( and read other details) at the Tamil Nadu Medical Council site.

All the best.