If you follow the
site walkthrough, the first detective case you'll complete is the
"Ground Zero" detective case. The 3 clues are in the following locations:
1 - Portion of a metal bracelet: Immediately after dropping down into the hole created by the explosive barrels that you hacked.
2 - Burned needle-nose pliers: When coming back to Cell Block C after acquiring the Batclaw, it's to the righht of where you dropped the elevator by cutting its broken cable. It's through a vent.
3 - Rubble fragments: In Cell Block C, on the bottom level, to the left, open the vent and enter it. It's inside the vent, just before exiting at the other end.