There is no way to "turn on case-sensitivity" for a single application. The filesystem structure on your volume is what's case-sensitive or not.
You can use Disk Utility to set this up, in a couple of different ways:
If you're just testing reading and writing files: make a disk image, using the format "Mac OS Extended (Case-sensitive, Journaled)". Mount that disk image and make your app use it.
If you want to test on a system booted from a case-sensitive filesystem: add a partition to your drive, choose the case-sensitive format for the new partition, then install OS X on it. Or use an external disk.
I'm sure there are more tricky ways, but those should get you started.