ACR FLC AT FL370 WERE ISSUED A DSCNT CLRNC BY ZDC CTLR. CREW LATER LEARNED THE DSCNT ALT WAS TO FL350 AND NOT FL250 AS READ BACK BY THE CREW.

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ACR XXX WAS PROCEEDING DIRECT SIE WHEN DIRECTED BY ATC TO 'CROSS 25 MI S OF SIE AT AND MAINTAIN FL350.' MY CAPT AND I HEARD THE AS XING 25 S OF SIE AT FL250. THE CAPT REPEATED THE CLRNC AS I HEARD IT '...25 MI S OF SIE AT FL250.' SINCE THERE WAS NO CORRECTING STATEMENT OR RESPONSE FROM ATC; I STARTED A RAPID DSCNT TO FL250; THE XING RESTR WOULD BE REQUIRED ALMOST AT A 4000 FPM RATE. PASSING THROUGH APPROX FL360-FL355; WE DECIDED WE WOULD NOT MAKE THE RESTR AT FL250 AND NOTIFIED ATC. ATC RESPONDED WITH AN AMENDMENT CLRNC TO MAINTAIN FL350. WE IMMEDIATELY INITIATED A CLB BACK TO FL350. AS THE ACFT HAD ALREADY DSNDED THROUGH FL350; THERE WERE NO RA'S OR HDG CHANGES REQUIRED. THE CTLR AFTERWARDS SAID IN A CASUAL VOICE THAT WE MAY HAVE HAD A SEPARATION PROB WITH ANOTHER ACFT. WE WERE SURPRISED BY THIS AS WE DID NOT GET ANY RA'S OF TFC ALERTS FROM THE TCASII OR ANY VECTORS FROM ATC. AFTER BEING PASSED ONTO THE NEXT FREQ; WE WERE ADVISED OF THE 'LOSS OF SEPARATION' OFFICIALLY. THE INCIDENT COULD HAVE BEEN AVOIDED IF THE CTLR HAD CORRECTED US ON OUR READBACK.