The measure heads to Republican Gov. Susana Martinez, who opposes it and vetoed similar legislation last year.
The proposal would allow a judge to expunge court and arrest records of victims of identity theft, people wrongly arrested for a crime and those convicted of misdemeanors if the individuals weren't charged with another crime within a certain period of time.
The measure wouldn't apply to crimes against children, sex offenses and drunken driving.
Supporters say public records of wrongful arrests can make it difficult for people to get jobs.
The bill won final approval Thursday when it passed the House on a 40-26 vote.