Independent contractors are businesses.
The general rule according to New Mexico state tax law and the Internal Revenue Code is that independent contractors are considered to be in business and they are self employed.

All businesses doing business within the state are required to register with the N.M. Taxation & Revenue Department to report their gross receipts (aka sales) in order to determine the amount of gross receipts tax for which they are liable.

Upon registration with the N.M. Taxation & Revenue Dept. businesses will receive their CRS ID number. This number is used to report gross receipts and NM payroll taxes. 

Caution: Your CRS ID number is a separate identification number from your IRS Employer Identification Number (EIN) and the Employer Account Number (EAN) which is issued by the NM Department of Workforce Solutions for reporting and paying state unemployment tax. Tip: When contacting a tax authority, be sure to use the ID number that agency has assigned to your business.

Businesses are also required to file income tax returns to report the share of their profit earned from doing business in New Mexico.