I am doing a project which involves connecting an android device with a separate Bluetooth module (AUBTMB20) which in turn is connected to a PIC controller. I am not able to figure out any code that establishes connection between the android and the Bluetooth module. The inbuilt class seems to only help with connection between two android devices. Is there any way to connect the mobile Bluetooth with a Bluetooth module?

You have there a nightmare of immense proportions.

My son did a bluetooth thing (in windows)for part of his bsce. He spent two weeks compiling versions of this or that and versions of bluetooth stack, and failed utterly. We broke our download limit with his googling and downloads. Going back to his lecturer they gave him another bluetooth dongle and it worked first time.

I tried bluetooth on my Android phone with my wife's iPad. They can see each other,(read ids, etc.) one sits back contentedly and says "Associated," while the other raises the middle finger :-(. Queries here and on mobile forums have produced no clues.
iPad - iPhone - no problem; Android - android or linux - no problem. Anything else - YMMV.

If they will both associate with a common intermediary, you might get going.