DHC8 Captain experiences a TCAS RA shortly after takeoff with the intruder aircraft collocated with zero altitude differential. The Captain elects to return to the departure airport with the TCAS annunciating 'descend descend' all the way to landing.

Narrative

On climb out; just a few feet past acceleration height; our TCAS started giving us erroneous RA's 'monitor vertical speed' followed by 'descend; descend' [and] a red square was displayed on top of our aircraft indicating that another airplane was on top of us. The TCAS gave us no proximate traffic call outs before this and no targets were displayed on it beforehand. All of a sudden a red square just appeared on top of our position. ATC said nothing of any other traffic being within our proximity and we could see no other traffic around us (VMC day) except for a 737 (which we had visual contact with) that had taken off before us and was about 10 miles to the SE of us and about 1;000 FT above us. We leveled off our altitude and told ATC of our malfunctioning TCAS and said we needed to return. ATC gave us vectors for the visual approach and all the way to the point of touchdown that red square with '00' on top of it was showing up on our TCAS; with resolution advisories of 'descend; descend' aurally warning us until we landed.