What was Rome's first non military police called?

Answer 1

The Vigiles Urbani (Watchmen of the City) or Cohortes Vigilum (cohorts of the watchmen) were both firefighters and police force.

In their police function, the Vigiles were the night watch. Their duties included apprehending thieves and robbers and capturing runaway slaves. They patrolled the streets and dealt mainly with petty crime and disturbances. They were a para-military force organised into cohorts and centuries like a legion. Violent crime and riots were handled by the Cohotes urbanae. These were like a heavy duty branch of the police. Their main role was to deal with roaming mobs and gangs that often haunted the streets of Rome during the Republic.

Alexander Severus added guarding the baths was added to the duties of the Vigiles as the baths remained open during the night.