Circumstances of unlocking the case: The case may become available while exploring the game world freely, in the region of The Bowery district (there will appear an appropriate notification on the screen, and the first entry concerning the case, in Batman's journal).
The place where the mission starts is the Jezebel Guns gun store, shown in the above screenshots. It is in the North-Eastern corner of The Bowery district. After you get there, listen to Batman's commentary and turn on the evidence scanner.
Stat by scanning the corpse of the man, who has been thrown off the roof (you need to hold down the key/button that the game prompts you to, each time), thanks to which you will determine his personals. Once again, scan the corpse, which will cause the virtual event reconstruction to be worked out.
Use the hook to reach the rooftop directly above the crime site, which has been shown during the reconstruction (you can now turn off the evidence scanner for a moment). Once here, scan the trace next to the destroyed fragment of the balustrade.
The last step in connection with the crime scene is using the reconstruction to find the suitcase. You need to start influencing the reconstruction's replay process by pressing the appropriate keys/triggers and observing the red line that symbolizes the item's trajectory. The suitcase is in the place shown in the screenshot, i.e. on the ledge below the roof with the destroyed balustrade. Scan the suitcase, thanks to which you will determine the murderer's personals.
This is not the end yet because, you still need to arrest Robert Hanes, i.e. the perpetrator of the crime. He is currently staying in the Diamond District in the South-Eastern part of the city. Since Hanes is among several of his allies, it is a good idea to preplan everything from above, to eliminate one of the bandits right at the outset.
After the fight proper starts, attack all of the enemies, including Hanes. This is, fortunately not too arduous a task. Leave the murderer for the end, because there will appear an option to interrogate him after you have sufficiently weakened him (pressing the appropriate key/button). Hanes will admit his crime and the investigation will be over.