3g is too small for any crayfish. It is also not the best environment for any crustacean. Shrimp, crabs, and crayfish are all extremely sensitive to nitrates , nitrites and ammonia. With a small volume of water, such as three gallons, there is no margin for error. You'll have to frequently monitor the water quality (every two to three days) and perform frequent water changes, to be safe.
If you're dead set on putting a large invert in the tank, you could possibly put in a single shrimp, from one of the smaller freshwater prawn species.