If you are engaged in business in New Mexico you are required to file the gross receipts tax there. But with zero income on a business that has already been shut down I don't know if you care if your right to do business in New Mexico is revoked.
In order to close your business with New Mexico and receive a certificate saying that the business is shuttered New Mexico will require that your filing is up to date.
You have no federal filing requirements if you have no income or expenses, however.
Here is the New Mexico information.
@jmburwardhoy