Circumstances of unlocking the case: This case may become available while freely exploring the game world, and more precisely the regions of the Park Row district (there will appear a notification on the screens and the entry concerning the mission will appear in Batman's journal). This mission will probably unlock after you have completed the game's campaign mode.
The location that this investigation starts in, is the crime scene, shown in the screenshot, in a small alley in the South-Eastern part of the Park Row district. After you get there, listen to Batman's commentary and turn on the evidence scanner.
First of all, you need to scan the corpses of the two victims, which will allow you to identify them. Remain here, scan the nearby blood trace and prepare the preliminary reconstruction basing on that.
You now need to press the keys/triggers to manipulate the reconstruction replay process and follow the red line that shows the bullet's trajectory. This will lead you to the venting shaft grate shown in the screenshot. Turn off the scanner, rip off the grate, activate the detective vision again and scan the bullet case that you find here.
Batman will automatically guess that the victims have been murdered by Ian Chase and you will have to arrest him. The murderer is in the southern part of the Industrial District. Since Ian it would be a good idea to plan the attack beforehand, so that you eliminate one of the bandits right at the outset.
After the fight proper starts, start attacking all of the enemies, including Chase. Fortunately, eliminating the enemies will turn out not to be too demanding. Leave the murderer for the end, because there will appear an option to interrogate him after you have weakened him sufficiently (press the key/button that appears on the screen). Although Ian does not confess, the case will officially close.