Thanks to an Indian "lurker" there is a book, which includes a chapter 'The Role of Police in Counterinsurgency Operations in Iraq, 2003–6' by Matt Sherman and the Abstract says:
Policing is a skilled and complex task that lies at the nexus of the security sector and the criminal justice system. Police are likely to be the face government presents to the population. They live and interact in the community within which they operate, are rarely unit-based, and have significantly different objectives and accountability structures than their military counterparts. This chapter highlights the challenges to the development of the Iraqi Police Services (IPS) during 2003–2006, as well as the Service’s failures and successes. Particular attention is paid to the politics underlying security at local and national levels, as well as mismatched Coalition and donor priorities (e.g. emphasizing quantity vs. quality), the comparatively lengthy and complex process of police and criminal justice sector development, the effect of strong leadership, the correlation between the growth of civil society and policing, and the role of host nation military support for policing.
The book is 'Policing Insurgencies: Cops as Counterinsurgents'. Edited by C. Christine Fair and Sumit Ganguly. Published by OUP (India) in 2013. See: http://www.oxfordscholarship.com/vie...4883-chapter-9

Matt Sherman was a US political adviser in Iraq 2003-2006, he spoke at a number of events and is now a SCI consultant.