MLG OVERSHOT ASSIGNED ALT IN DSCNT CAUSING LTSS AND TCASII RA.

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RECEIVED A CLRNC TO DSND DOWN TO 6000 FT. I SELECTED 6000 FT IN THE ALT WINDOW AND POINTED TO IT TILL THE CAPT ACKNOWLEDGED BY MOVING HIS HEAD AS IF SAYING OK. (THIS IS NORMAL PROC FOR ALT AWARENESS AT MY AIRLINE). THE AUTOPLT HAD BEEN SELECTED FOR MOST OF THE FLT AND IT WAS ON AT THIS TIME. AFTER CAPT ACKNOWLEDGED NEW ALT (HE'S STILL ON PA) TO ME; I INITIATED THE DSCNT. WHEN CAPT FINISHED HIS PA; I SAID 'GOING DOWN TO 6 OTHERWISE NO CHANGES.' AT 6000 FT APPROX 4-6 MINS APCH CTL AT ROC SAID TO US 'ACR YOU WERE ASSIGNED 7000 FT' AND THEN GAVE DSCNT INSTRUCTIONS TO ANOTHER ACFT. AT THE SAME TIME TCASII ISSUES A 'DSND NOW' RA (NO TA INVOLVED ONLY RA). AS I INITIATED THE DSND AND STARTED DOWN THE TCASII ISSUED A 'CLB NOW' RA. SO WE WENT THE OTHER WAY. WE STARTED TO CLB TO BE IN COMPLIANCE WITH TCASII. THE CLOSEST I SAW THE CONFLICT ON TCASII WAS 500 FT BELOW AND ABOUT 1-2 MI AT 1-2 O'CLOCK. CAPT THEN ASKED APCH 'WHERE DO YOU WANT ACR?' APCH HESITATED FOR A MOMENT AND THEN SAID 6000 FT HDG 040 DEG -- WHICH IS WHERE WE HAD BEEN. ON THE GND WE PHONED TRACON AND SUPVR SAID HE HAD LISTENED TO THE TAPES AND THEY INDICATE THAT WE WERE ASSIGNED 7000 FT AND READ BACK 7000 FT. ALL I CAN SAY IS THAT NO ONE IS PERFECT AND I REALIZE THAT BUT I CANNOT RECALL BEING GIVEN 7000 FT BUT I DO RECALL RECEIVING 6000 FT AND READING BACK 6000 FT AS I SELECTED 6000 AND POINTED AT IT -- TILL CAPT ACKNOWLEDGED. THERE IS NO DOUBT IN MY MIND ABOUT THIS. IF I HAD A LITTLE BIT OF DOUBT THEN I THINK 'OK MAYBE I DID' -- BUT THERE'S NO DOUBT! IN CLOSING I'LL SAY THAT ANYTHING IS POSSIBLE AND IF I BLEW IT; THEN IT WAS AN HONEST MISTAKE. SUPPLEMENTAL INFO FROM ACN 221138. CPR JET GIVEN 6000; WAS CLBING TO THAT ALT.