An air carrier First Officer reported a go-around from 300 FT on approach to LGA's Runway 22 because Tower released an aircraft for takeoff on Runway 31 that would conflict with them during landing.

Narrative

We were cleared for the visual to Runway 22 at LGA. The aircraft was configured fully. Approximately three miles out; we were cleared to land number one for the runway. At approximately a 1/4 mile final or around 300 FT Tower advised us that Air Carrier Y would be departing left to right on Runway 31. This took myself and the Captain by surprise as were were short final and couldn't fathom that they were clearing an aircraft for takeoff and immediately saw this as a conflict. After we were able to make a visual that in fact they had cleared an airplane for takeoff; the First Officer (flying pilot) immediately initiated a go-around with a hard left climbing turn to avoid potential collision. The go -around was conducted with greater than standard bank in order to prevent flying into the departure path of the Air Carrier Y. We were climbed to 2;000 with no RA's noted. We were then vectored back to the ILS 22 and landed without incident. The Departure Controller vectoring acknowledged and commented on the close proximity to the departing aircraft when we checked back in for the second approach. Nothing said by the Tower. Everything always occurs on day 4!