ACR X TCASII RA DSND HAD LTSS FROM SMA Y. SYS ERROR. EVASIVE ACTION TAKEN.

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I WAS WORKING LCL CTL AND HAD BEEN ON THE POS FOR ABOUT ONE HR. IT WAS JUST AFTER A BUSY DEP PUSH. I CLRED ACR X FOR TKOF ON RWY 15R AND ISSUED A R TURN HDG 330 DEG AT 1 DME. APCH WAS BRINGING SMA Y FOR AN APCH TO RWY 4; A NONSTANDARD RWY NOT ACTIVE AT THE TIME. THERE WAS NO COORD ON THESE OP. THE FIRST TIME I WAS AWARE OF A PROBLEM WAS WHEN APCH CALLED AND ASKED IF I HAD THE SMA Y IN SIGHT. I DID NOT. ON INITIAL CONTACT I CALLED TFC TO SMA Y AND HE RPTED THE ACR IN SIGHT. HOWEVER BY THAT TIME SEPARATION WAS ALREADY LOST. I FEEL THE BASIC CAUSE OF THIS PROBLEM WAS THE FAILURE OF PROPER COORD AND MY INATTENTIVENESS TO WATCH ALL MY AIRSPACE ALL THE TIME. IN ADDITION THE ACR RECEIVED A TCASII RA THAT TOLD HIM TO DSND BELOW THE TFC. I FEEL IF HE KEPT CLBING HE WOULD HAVE CLRED THE TFC NO PROBLEM. SUPPLEMENTAL INFO FROM ACN 209902. ACR X DEPARTING RWY 15R; TURNING R AND CLBING OUT DURING DEP; RECEIVES TCASII ALERT ON SMA ACFT DSNDING VFR INTO RWY 4. ACR X REACTS TO ALERT; LEVELING THEN DSNDING BELOW VFR ACFT. IN MY OPINION; HAD ACR X CONTINUED CLBOUT; NO ERROR WOULD HAVE OCCURRED. ADDITIONALLY; IT IS MY UNDERSTANDING; THAT THE ACR X CREW HAD THE SMA Y IN SIGHT AND STILL RESPONDED TO THE TCASII COMMAND.