THE PLT WAS CLRD FOR AN IFR DEPARTURE FROM RWY 16 IN INSTRUMENT METEOROLOGICAL CONDITIONS (IMC). HIS DEPARTURE CLNC WAS TO CLIMB ON RWY HEADING TO 800 FT, THEN TURN RIGHT TO A HEADING OF 320 DEG. WHEN THE ACFT TOOK OFF, TOWER PSNL DID NOT HAVE VISUAL CONTACT WITH THE ACFT, & ASKED THE PLT TWICE, IF THE ACFT WAS AIRBORNE. AFTER THE 2ND INQUIRY, THE PLT ACKNOWLEDGED THAT HE WAS AIRBORNE; HE WAS THEN INSTRUCTED TO CHANGE TO DEPARTURE FREQ. THE PLT ACKNOWLEDGED THE FREQ CHANGE. THEN, ABOUT 35 SEC LATER, AN ELT SIGNAL WAS HEARD. A SEARCH WAS INITIATED & THE ACFT WAS FOUND ABOUT 1/2 MI SOUTH OF THE TOWER. WITNESSES, WHO HEARD THE ACFT, RPRTD THAT AFTER TAKEOFF, THE ACFT APPEARED TO ENTER A CIRCLING MANEUVER AT LOW ALT, THEN CRASHED. NO PREIMPACT MECHANICAL PROBLEMS WERE FOUND WITH THE ACFT. WX AT THE TIME OF THE ACDNT WAS IN PART: INDEFINITE CEILING, 100 FT OBSCURATION, VIS 1/2 MI WITH FOG, WIND FROM 110 DEG AT 10 KTS.