The Kingston NY Police Department is located at 1 Garraghan Drive, call 845-331-1671 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 Ulster County Sheriff's nearby facility.