SMA AT NON TWR ARPT ANNOUNCED DEP ON CTAF. NON RESPONSE. ON TKOF HEARS SECOND ACFT ANNOUNCE DEP OPPOSITE DIRECTION. EVASIVE ACTION REQUIRED.

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AS PIC OF OUR SMA; I WAS INVOLVED IN A NEAR MISS AT COTTONWOOD ARPT (P52); COTTONWOOD; AZ. MY HUSBAND (ALSO A PLT) AND I HAD BEEN ATTENDING AN ANTIQUE AIRPLANE AND AUTO SHOW IN THE TIEDOWN AREA AT THE ARPT. THE WX WAS CAVU WITH MANY ARRS AND DEPS; USUALLY LNDG ON RWY 32 AND ALSO DEPARTING ON RWY 32; DOWNHILL AND TO AVOID OVERFLYING MANY HOMES W OF RWY 14. WHEN WE DECIDED TO LEAVE AROUND NOON TIME; WE BOARDED THE SMA AND BEFORE TAXIING OUT TO THE ACTIVE (WHICH WE THOUGHT WOULD CONTINUE TO BE RWY 32); WE ANNOUNCED TO TFC; IN THE BLIND; OUR INTENTIONS. WE HEARD NO COMMENT FROM UNICOM OR OTHER TFC; OR FROM PARKING ASSISTANTS IN THE TIEDOWN AREA. UPON REACHING RWY 32; I DID THE NORMAL RUNUP AND BEFORE TAKING THE ACTIVE; MY HUSBAND AND I BOTH LOOKED FOR TFC. NO ONE ANNOUNCED ON THE RADIO FOR LNDG OR TAKING OFF. WE THEN ANNOUNCED TAKING THE ACTIVE AND IMMEDIATELY DEPARTED RWY 32. A FEW SECONDS LATER; WE HEARD A PLT ANNOUNCE HE WAS DEPARTING ON RWY 14. WE WERE ALREADY AIRBORNE WHEN WE SAW AN SMA B ACFT HDG TOWARDS US ON RWY 14. I VEERED SHARPLY TO THE R; THE OTHER PLT PASSED BELOW US AND VEERING TO HIS R. NO BUILDINGS; OTHER PLANES OR SPECTATORS WERE ANYWHERE NEAR US. MY HUSBAND IMMEDIATELY CALLED UNICOM TO SEE IF OUR RADIO WAS FUNCTIONING AND THE FBO SAID HE HAD HEARD OUR TRANSMISSIONS; BUT WAS IN THE MIDST OF CHANGING RWYS BECAUSE OF WINDS OUT OF THE SW. THE OTHER PLT NEVER DID SAY ANYMORE ON THE RADIO. I DID NOT CONFIRM THE ACTIVE RWY WITH UNICOM BEFORE TAXIING OUT. I ASSUMED IT WAS RWY 32 AS USUAL AND WITH THE DENSITY ALT AND POOR CLB RATE OF THE SMA; I PREFERRED A DOWNHILL DEP. NOT SEEING ANY OTHER ACFT; I DID NOT WAIT AND CONFIRM THE CORRECT RWY BEFORE DEPARTING; I ANNOUNCED TO TFC BUT DID NOT VERIFY.