Circumstances of unlocking the case: You may get the opportunity to complete this mission while freely exploring the game world, especially the Burnley district. It should unlock automatically right after you have visited the police morgue, and left the sewers after you complete the Scan the corpse in the GCPD morgue mission (you will receive a notification on the screen, and there will appear a new entry in Batman's journal).
The starting point for this investigation is the crime scene shown in the above screenshots, located in the central part of the Burnley district, to the North of the police precinct. After you get there, listen to Batman's commentary and activate the evidence scanner.
Start by scanning the corpse of the man who was run over with a car, thanks to which you will learn that he was a policeman.
Take a look around the corpse for traces of blood and scan them, which will result in the preparation of the initial version of events. Another blood trace can be found a bit further and it will help you determine a more detailed version.
You now need to use keys/triggers to manipulate the reconstruction playing process. Your task is to determine the possible route of the car that ran over the man. This will allow you to locate the trace shown in the above screenshot, which can also be scanned (you need to hop over the barriers to get there). Thanks to having scanned the trace, Batman will determine that the car belonged to a corrupt policeman.
This is not the end yet, because you need to arrest John DeMarco, i.e. another SWAT member, responsible for the murder. The man that you are looking for is on the rooftop of one of the buildings in the [Burnley] district, to the North-east of the crime scene. Since John is surrounded by his allies, you need to be careful, especially that the roof where you are going to fight is small.
DeMarco himself is also using armor so, stun him with the cape or use other attacks that are effective while weakening the armored enemies. Leave this man for the end because there will appear an option to interrogate the policeman after you have weakened him sufficiently (by pressing the appropriate key/button). DeMarco will admit to his deed and the interrogation will end.