AT AN UNCTLED ARPT A PLT APPARENTLY NOT MONITORING CTAF; CONTINUED HIS APCH AND LANDED ON A XING RWY AFTER AN ACFT ANNOUNCED TKOF INTENTIONS. TKOF REJECTED BY RPTR.

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MR X AND I ABORTED A TKOF IMMEDIATELY AFTER ADDING FULL PWR AND RELEASING THE BRAKES AT HTO ARPT. I'M THE ASSISTANT CHIEF PLT AND MR X IS ONE OF OUR SENIOR INSTRUCTORS. (WE WERE DOING A BREAK-IN FLT FROM HTO TO FRG.) SE DECIDED TO USE RWY 28 FOR TKOF SINCE THE WINDS WERE FROM THE W AND WE HEARD OTHER AIRPLANES USING RWY 28. AFTER OUR RUN-UP WE MONITORED THE FREQ AND I CHKED THE APCH END AND ANNOUNCED 'EAST HAMPTON TFC; CESSNA TAKING THE ACTIVE RWY 28 FOR DEP; EAST HAMPTON TFC.' AFTER NO RESPONSE; MR X TAXIED ONTO THE RWY; ADDED FULL PWR AND RELEASED THE BRAKES. AS SOON AS HE STARTED THE TKOF ROLL; I NOTICED THAT A CESSNA WAS COMING UP ON SHORT FINAL FOR RWY 22. I IMMEDIATELY TOLD MR X TO STOP AND WE ABORTED THE TKOF. THE OTHER CESSNA CONTINUED TO LAND 1/2 WAY DOWN THE RWY. AFTER LNDG; THE CESSNA'S PLT STATED HE CALLED ON A 1 MI FINAL. MR X REPLIED 'WE DIDN'T HEAR ANYTHING' AND THE OTHER PLT RESPONDED 'OH.' WE TAXIED OFF THE RWY AND PROCEEDED BACK TO THE APCH END OF RWY 28 FOR TKOF. I DO NOT BELIEVE THE CESSNA PLT CALLED ON A 1 MI FINAL LIKE HE CLAIMED AND WHEN HE HEARD US TAKING THE ACTIVE RWY 28 HE SHOULD HAVE SAID SOMETHING. FURTHERMORE; HE SHOULD HAVE BEEN USING THE SAME RWY EVERYONE ELSE WAS USING AND HE SHOULD HAVE DONE A GAR WHEN HE HEARD US ABORT OUR TKOF.