Jonathan Paul, 42, was arrested last week on outstanding misdemeanor warrants.
While in jail, officers reported Paul became combative and wouldn't follow orders.
Detention officers placed him in an isolated cell and later noticed he was non-responsive.
He was taken to a hospital, where he died.
The Arlington Police Department has launched both the criminal and administrative investigations, but detectives won't comment until they get a ruling from the medical examiner on Paul's manner and cause of death.
Police confirmed there is jail surveillance video, but they won't release it until the investigations are completed.