What is the criminal  justice system invovlement in public policy?:
I assume you are referring to the entire criminal justise system as the professional group.

As in the series Law and Order it involves enforcement as well as the legal profession.  Part of the system is the law makers as well.

Public policy is not always easy to define.

Power and influence in an ideal democaracy would come from the people but we know that isn't really true, eoungh money will sway public opinion and buy almost any election and swing almost any vote whether it is public or in legistature.

I am not sure what you mean by "playing policy roles"

The direct enforcers offer direct power.  The police and the judges.  But those who actually make the laws provide the true power and that comes back to the people with money to buy the influence to change laws.  

It really all goes back to the rich and powerful.