If you are an NRI you probably can't apply for NATA .Because for Nata you have to given exam from the resoective centre
Coming to your domicile certificate.
If you are already presiding in a state from the time of your birth and haven't moved from that place since you won't require Domicile
In that case your school certificate can also act as a proof of you residing in that place
If you have changed your place since its better to get your domicile done,it can be received within 15 days.
Just go through NATA guidelines if they have mentioned that ypu are required to show that document you can get it done,else you can submit some other document that suffices its purpose
I hope this helped
While during registration, there is no any such tab for domicile. But i suggest you to go through the brochure of NATA carefully and properly. For your convinience purpose here is the link for NATA brochure:
It is in PDF format. Hope this helped.
Thank you. All the best!!