Which is the "competent authority" for investigating a crime such as abduction in Pakistan

“Which is the "competent authority" for investigating a crime such as abduction in Pakistan? 

“Competent Authorities” for Investigation & Enforcement suffer from conflicts of jurisdiction, duplication, redundancies, multiple chains of commands, and mismatch of authority with responsibility. There is lack of transparency, and accountability. There is a perennial tension between Enforcement vs Investigation induced by the ends vs means dichotomy! Enforcement requires immediate action and is dominated by the need for "results" (ends) over the need for "due process" (means). However, investigation leading to conviction by courts requires meticulous attention to "due process" (means) over the need for "results" (ends). 

Due process requires education and training. It requires knowledge of criminology, logical deduction, intricacies of law and piecing together of clues and power of observation and awarness of crime psychology. This is the  reason why Scotland Yard makes reading of Sherlock Holmes and Hercule Poirot mandatory for investigators. 

Unfortunately there is no such training for investigation agencies. They are driven by Gestapo type of "results" and are dominated by the "chhitrol" (چھترول) mentality of SHO's in the "thana" culture. They have all the  authority with no responsibility. The responsibility mish-mash is visible from the plethora of investigation agencies as given in the attached diagram. 

For example: Which “Competent Authority” is responsible for investigating an Abduction اغوا?

Who is to be held responsible for lack of investigation, and inability to catch the culprits? Who should the PM  punish for investigation failure of an abduction?

There are overlapping responsibilities among ICT Police, DMGs, Secretary Interior Ministry, Secretary Defense Ministry, Crime Branch, Special Branch, Elite force, CID (Crime Investigation Department), CLC,….. National Counter Terrorism Authority, Anti Narcotic Force, Frontier Constabulory, Rangers, Intelligence Bureau, Military Intelligence, ISI, ISPR, FBR Investigation Unit, NAB, FIA, …or Chief, Minister of  Interior of Defense, PM himself. Or CM to whom the Home Department reports under which provincial police departments operate.