B737-300 CREW HAD AN AIR-GND FAILURE. THE LNDG GEAR WOULD NOT RETRACT BEYOND THE LEVER LATCH; OFF; POS; AND THE TKOF WARNING HORN ACTIVATED.

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ON FLT TO ZZZ AFTER TKOF WHEN FLAPS WENT FROM 1 DEG TO UP THE TKOF WARNING HORN CAME ON. THE HORN ACTED AS IF THE JET WAS ON THE GND. ALL OTHER INDICATIONS WERE NORMAL FOR FLT. CONTRACT MAINT WAS CONTACTED. HE CLEANED THE SPD BRAKE CONTACTS AND SAID THE PROB WAS RESOLVED. ON DEP FROM ZZZ AFTER TKOF; WE WERE UNABLE TO RAISE THE GEAR HANDLE PAST OFF; AND WITH THE FLAPS UP WE HAD THE TKOF WARNING HORN. WE SUSPECTED THERE WAS AN AIR/GND SENSOR PROB AND I BELIEVE BOTH PROBS WERE RELATED. WE WENT THROUGH THE 'GEAR LEVER WILL NOT MOVE UP AFTER TKOF' CHKLIST. WE TOLD DEP WE WERE RETURNING BACK TO ZZZ BUT WE WERE NOT DECLARING AN EMER NOR DID WE NEED ASSISTANCE. AS PER THE CHKLIST; I PULLED THE CIRCUIT BREAKERS AND THEN RESET THEM TO MAKE SURE WE HAD 3 GREEN FOR LNDG. THE TKOF WARNING HORN DID NOT SOUND; SO I RAISED THE GEAR HANDLE AND THEY CAME UP. ALL INDICATIONS WERE NORMAL IN THE COCKPIT. I THEN TOLD DEP WE NEEDED A VECTOR. I CONTACTED DISPATCH AND TOLD THEM WE WOULD LIKE TO PROCEED TO DEST. THEY CONFERRED WITH MAINT AND SAID IT WAS OK. WE ENDED UP DOING A COUPLE OF 360 DEG TURNS AT ABOUT 7000 FT. WE THEN PROCEEDED TO DEST AND THE FLT WAS NORMAL. I TOLD DISPATCH TO HAVE CONTRACT MAINT READY AT DEST. I WROTE THE JET UP AND HANDED IT OFF TO CONTRACT MAINT AND THE NEXT CREW. I AM SUBMITTING THIS LATE BECAUSE I THOUGHT I HAD DONE THE CORRECT ACTION. AFTER JUST TALKING WITH A CHIEF PLT ON THE PHONE; I SHOULD HAVE RETURNED TO ZZZ. THE QRH GIVES NO RELIEF FOR CONTINUING. EVEN THOUGH I HAD ALL NORMAL INDICATIONS IN THE COCKPIT; THE CHKLIST SAYS ONCE I HAVE THE PROB IT IS COMPANY POLICY TO RETURN TO DEP CITY UNLESS THE AIRFIELD IS UNSUITABLE. HAD THE TKOF WARNING HORN STILL BEEN ON WHEN I RESET THE CIRCUIT BREAKERS; I WOULD HAVE FOLLOWED ON WITH THE CHKLIST AND RETURNED TO ZZZ DUE TO THE FACT ALL INDICATIONS IN THE COCKPIT WERE NORMAL AND HAVING LULLED ME INTO THINKING I HAD A GOOD JET AND WAS TO FLY TO DEST. HOWEVER; THERE MIGHT HAVE BEEN A FURTHER MALFUNCTION ENRTE AND MIGHT HAVE HAD MORE SERIOUS PROBS. SUPPLEMENTAL INFO FROM ACN 613102: PRESSURIZATION WAS NORMAL THROUGHOUT THE EVENT. AT AN INTERMEDIATE LEVELOFF ALT; WE DETERMINED THAT ANY TIME PWR WAS RETARDED BELOW APPROX 80% N1; THE HORN STOPPED. AS PF; I FLEW AND COORDINATED WITH ATC WHILE THE CAPT WENT THROUGH THE QRH AND NOTED THAT THE QRH REQUIRES A 'RETURN TO THE DEP ARPT UNLESS WX OR RWY CONDITIONS PRECLUDE A RETURN.' AT SOME POINT DURING HIS ACTIONS; THE LNDG GEAR HANDLE WAS RETRACTED AND THE GEAR RETRACTED NORMALLY. I DIDN'T FEEL THERE WAS A SAFETY OF FLT ISSUE ALTHOUGH I WAS CONCERNED THAT THE QRH DID NOT GIVE US THE LEEWAY TO CONTINUE. I YIELDED TO THE DECISION MADE BTWN THE CAPT; DISPATCH; AND MAINT TO CONTINUE. IN HINDSIGHT; I SHOULD HAVE GOTTEN INTO THE CHKLIST MYSELF TO BACK HIM UP. I'M NOT SURE I WOULD HAVE BEEN WILLING TO OVERRIDE THE JOINT DECISION.