The Law:

Felons on probation, in prison, or on parole cannot vote. In 2001, the legislature passed legislation repealing the state's ban on voting by people who have completed their sentences. In 2005, a bill was passed that requires the Department of Corrections to provide notification of completion of sentences to the Secretary of State’s office.

Getting Your Vote Back:

http://www.sentencingproject.org/pdfs/rights-restoration/NewMexico.pdf