You should check out /u/XenophontheAthenian's answer on How did Republican Rome function without a police force? and What did the Vigiles do and how similar were they to a police force?

Both are highly recommendable and should answer your questions.

Bit busy with my Latin America essay right now so I can't write a lengthy answer, but do check out Nippel's article 'Policing Rome'. It highlights the importance of the general populace as a whole in maintaining civic order in Republican Rome, especially during the 'revolts' of Saturninus and the Gracchi. Maybe someone can help summarize the article?

Wilfried Nippel, 'Policing Rome', The Journal of Roman Studies, Vol. 74 (1984), pp. 20-29 http://www.jstor.org/stable/299004