Buying a car without address proof in the state one is buying it from

I've been living in Auroville, Tamil Nadu in a guest house for 2.5 months. I want to buy a car here (the nearest showrooms are in Cuddalore and Chennai).

All my documents mention my address in Delhi. I don't have a rent agreement with the guest house, I simply pay rent at the beginning of the month.

Any idea how I can do this?

Would an affidavit signed by a notary saying I live in XYZ Guest House, Auroville, be enough?

Or would I need to get a rent agreement?

Is it possible that the dealer gets the car registered in Delhi rather than in TN?