No Due Process Right to Adequate Police Investigation

If your child died, you'd expect the police to adequately investigate your child's death.  This is a reasonable expectation, as you are a taxpayer.  It's also the case that rich and connected people receive thorough police investigations.  Thus, an average American family believes that police should find out who killed their child.

The caselaw on this point is well-established.  As a matter of federal constitutional, there is no right to an adequate police investigation:

The question presented is whether citizens of Suffolk County, New York, have a propertyinterest protected by the Due Process Clause of the Fourteenth Amendment in adequate police investigations. Plaintiffs-appellants Thomas and Ann Marie Harrington (“plaintiffs”) appeal from a judgment of the United States District Court for the Eastern District of New York (Leonard D.Wexler, Judge) dated August 18, 2009 dismissing their complaint pursuant to Fed. R. Civ. P. 12(b)(6). Plaintiffs claimed that defendants-appellees (“defendants”) had violated their constitutional rights byfailing to conduct an adequate investigation into a traffic accident that resulted in the death ofplaintiffs’ son.
We hold that the Suffolk County Code does not confer on plaintiffs a constitutionally protected property interest in an adequate police investigation. Although the complaint alleges police conduct that is far from satisfactory, it does not allege misconduct rising to the level of a violation of the United States Constitution. 
Harrington v. County of Suffolk (CA2) (here).  Hire your own private investigators.  You can't afford that?  Tough luck.

While there is no constitutional right to an adequate police investigation, there is a de facto privilege to one.   See United States v. Aleynikov (Goldman Sachs has a direct line to the FBI, and thus claims of employee misconduct are handled within 48 hours of a phone call.)