The company's accountant should be able to help you process this paperwork with the IRS. In New Mexico, Certificates of Incorporation do not require that officers be named. However, if they require that directors be named, you'll want to file a certificate of change, reflecting that you are no longer a director.
Most importantly, though, you'll want to have a written agreement with the other (and remaining) owner of the company concerning your departure. Are you entitled to be paid any money? If so, how much and over what period of time? Are there any restrictions on your use of the company's customer list or intellectual property? Has your name been taken off all of the company credit lines and other obligations?
A local business attorney can help you iron out all of these details so that there are no loose ends to come back to haunt you years from now.