FLC OF A CPR JET DEVIATED FROM ASSIGNED ALT WHEN DISTRACTED IN TROUBLE-SHOOTING AN ACFT EQUIP PROB.

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WE DEPARTED OMA AT XB00 TO RETURN TO GXY. THIS WOULD BE OUR 5TH AND FINAL LEG OF THE DAY THAT BEGAN AT XA00. HAVING ARRIVED AT OMA WITHIN THE PAST HR WE KNEW FIRST HAND OF THE TSTM ACTIVITY IN THE AREA. AFTER CHKING WITH FLT SVC BEFORE DEP; IT WAS DETERMINED A FLT S OF OUR INTENDED COURSE WOULD ALLOW US TO AVOID THE WORSE TSTM ACTIVITY AND THEN CONTINUE TO GXY. AFTER A NORMAL TKOF AND CLB WE WERE SOON IMC AND USING THE ON BOARD WX RADAR TO CIRCUMNAV TSTMS. ALL ANTI-ICE SYS WERE TURNED ON PRIOR TO ENCOUNTERING ICING CONDITIONS. UPON REACHING OUR ASSIGNED ALT OF FL390 AND BEGINNING TO LEVEL OFF THE ACFT OVERSPD AURAL WARNING WAS ACTIVATED. XCHKING THE AIRSPD INDICATORS SHOWED THE CAPT'S AIRSPD NORMAL AND THE COPLT'S AIRSPD HIGH. ENGAGING THE AUTOPLT TO TROUBLE- SHOOT THE OVERSPD WARNING; THE ALT HOLD DID NOT ENGAGE AND THE AIRPLANE DSNDED FROM FL390 TO FL380. ZMP WAS ADVISED WE WERE HAVING A PROB AND WE REQUESTED AND WERE ASSIGNED FL350. WE LEVELED AT FL350; GOT THE AURAL OVERSPD SILENCED AND CONTINUED THE FLT. AS OUR TRAINING HAS EMPHASIZED 1 PLT NEEDS TO FLY THE AIRPLANE AND 1 PLT ATTENDS TO THE PROB. BOTH OF US ATTEMPTING TO DO 1 TASK ALLOWED THE ACFT TO DEVIATE FROM ASSIGNED ALT. USING THE ACFT AUTOPLT TO HELP SOLVE THE PROB DID NOT RELIEVE ME OF THE DUTY TO MONITOR THE ACFT. LET EACH CREW MEMBER DO THEIR JOB.