AN MD80 EXPERIENCED LARGE HDG ERRORS ON BOTH CAPT'S AND FO'S HSI'S BEFORE AND DURING TKOF AT LGA.

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MIDWAY THROUGH OUR TKOF ROLL WE HAD ERRONEOUS HDG INFO THAT CAUSED THE HDG ANNUNCIATOR TO COME ON. WE DEPARTED FROM LGA RWY 13. RWY 13 HAS A SIGN THAT REMINDS YOU TO PREPARE FOR THAT POSSIBILITY. WE DID; HOWEVER WE WERE CLRED FOR IMMEDIATE TKOF AND AS BEST I COULD TELL HAD CORRECT HDGS. THE REASON FOR THIS IS THAT WE ARE NOT SURE IF WE COMPLIED WITH THE NOISE ABATEMENT OF LGA. AFTER TKOF WE TURNED R TO 175 DEGS ON THE FO'S SIDE. HIS DID APPEAR LATER TO BE THE CLOSER OF THE TWO. WE HAD THE WHITESTONE CLB AND AT 2.5 MI WE THEN TURNED TO 040 DEGS. IT WAS HERE THAT WE HAD TIME TO REF THE MAGNETIC COMPASS. AT THAT TIME IT SHOWED THE FO'S SIDE TO BE ABOUT 10 DEGS OFF AND MY SIDE TO BE PROBABLY 30 DEGS OFF. WITHIN APPROX 10 MINS THE SYS CORRECTED ITSELF. THIS IS DEFINITELY A PROB AT LGA ON RWY 13. MAYBE IT WOULD BE A GOOD IDEA TO PUT SOME TEXT INTO OUR COMPANY PAGES ABOUT THIS HAPPENING ON RWY 13 AND THAT IF NEEDED YOUR HDG INDICATORS SHOULD BE MANUALLY SLAVED TO THE RWY HDG. SUPPLEMENTAL INFO FROM ACN 366912: WHILE IN POS AND HOLD LGA RWY 13; CAPT'S HSI DRIFTED OFF APPROX 30 DEGS AND FO HSI DRIFTED OFF APPROX 10 DEGS. DEP WAS FLOWN OFF STANDBY COMPASS FOR APPROX 10 MINS UNTIL BOTH HSI'S WERE ALIGNED AGAIN. BELIEVE NO SIGNIFICANT DEP DEVS OCCURRED AS NEITHER LGA TWR NOR NEW YORK DEP MADE ANY COMMENTS. REST OF FLT WAS NON EVENTFUL. BELIEVE TIME SITTING OVER PYLINGS AT END OF RWY MAY HAVE PULLED HSI OUT OF ALIGNMENT.