Do you have to tell the state you sold it?
Yes. Mail MVD-10048, Notice of Vehicle Sold. No deadline is stated.
State law says you must notify MVD of the sale. MVD's form for this is MVD-10048, Notice of Vehicle Sold. It asks for the date sold, the buyer's name and address, and the vehicle. Mail it to Motor Vehicle Division, Attn: Sold Unit, P.O. Box 1028, Santa Fe, NM 87504-1028. Neither the law nor the form sets a deadline. Separately, you remove the plate. MVD gives you 30 days to put it on another vehicle of the same class or return it for cancellation.
Source: N.M. Stat. § 66-3-101(A); form MVD-10048 Rev. 08/14; NM MVD Procedure Manual ch. 4 §B