The Alamogordo NM Police Department is located at 700 Virginia Ave, call 575-439-4300 to find out about new arrests or outstanding warrants. This is a police jail for housing inmates immediately after their arrest. Local police departments are not built for long-term inmate holding, they are for very short-term stays because there are not enough cells. There are no visits, commissary or phone accounts available to the offenders.
If they are to remain incarcerated, it will be most likely to the Otero County Sheriff's nearby facility.