DURING ARRIVAL TO THE KANSAS CITY DOWNTOWN ARPT, THE FLT WAS VECTORED FOR A VOR RWY 3 APCH, THEN WAS CLEARED FOR THE APCH & TO CIRCLE & LAND ON RWY 36. ON FINAL APCH, THE ACFT WAS HI & WAS NOT IN A POSITION TO LAND, SO THE FLT WAS CLEARED TO CIRCLE LEFT FOR ANOTHER APCH TO LAND. THE AIRCREW ACKNOWLEDGED & BEGAN CIRCLING LEFT WHICH TOOK THEM IN THE VICINITY OF THE FAIRFAX ARPT. A SHORT TIME LATER, THE ATC CONTROLLER CAUTIONED THAT THE FLT MIGHT BE LINING UP FOR THE FAIRFAX ARPT. SUBSEQUENTLY, THE CREW INITIATED A MISSED APCH & WERE INSTRUCTED TO TURN TO 360 DEG & CLIMB TO 3000 FT. THE ACFT BEGAN A STEEP CLIMB TO 3100 FT, STALLED & ENTERED A STEEP DESCENT. BEFORE THE DESCENT WAS ARRESTED, THE ACFT IMPACTED IN A PUBLIC WATER TREATMENT PLANT. CVR RECORDINGS INDICATED THAT THE 1ST OFFICER WAS FLYING THE ACFT DURING THEEN ROUTE DESCENT, VOR APCH & CIRCLING APCH, THEN THE CAPTAIN TOOK CONTROL DURING THE MISSED APCH. AN EXAM OF THE WRECK- AGE REVEALED NO EVIDENCE OF AN AIRFRAME OR POWERPLANT PROBLEM. ALSO, THERE WAS NO EVIDENCE THAT THE CARGO HAD SHIFTED.