C182 PLT DEPARTING STRAIGHT OUT ON RWY 27 AT CDW EXPERIENCES NMAC WITH C172 IN TFC PATTERN FOR RWY 22.

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I WAS CLRED FOR TKOF ON RWY 27 BY CDW TWR. I WAS FLYING MY C182S SOLO VFR TO N07 (APPROX 5 NM TO THE N) TO DROP OFF THE AIRPLANE FOR AN OIL CHANGE. ANOTHER ACFT (A C172) WAS DOING TOUCH-AND-GOES ON RWY 22. BOTH ACFT WERE UNDER THE CTL OF CDW TWR (A NON RADAR FACILITY). I HAVE A GTX 330 INSTALLED IN MY ACFT BUT MY ALT WAS TOO LOW TO PICK UP A TFC ALERT. SEVERAL OTHER ACFT WERE CONTACTING THE TWR PRIOR TO ENTERING THE CLASS D AIRSPACE FOR LNDG; AND A FEW HAD RECENTLY LANDED. THE AFD SPECIFIES THE FOLLOWING FOR DEPS AT CDW: RWY 27 (R TFC) FROM DEP END; RWY HDG FOR 1 MI THEN...IF DEPARTING PATTERN CONTINUE STRAIGHT OUT OR EXIT WITH A 45 DEG R TURN AFTER REACHING PATTERN ALT. RWY 22 (R TFC) FROM DEP END TURN R HDG 230 DEGS UNTIL 900 FT MSL THEN IF REMAINING IN THE PATTERN TURN TO XWIND.... AS YOU MIGHT PREDICT FROM THE FOREGOING; AT 1100 FT MSL CONTINUING STRAIGHT OUT AND LESS THAN 1 MI FROM THE DEP END OF RWY 27; UPON LOWERING THE NOSE BRIEFLY; I SAW THE SECOND ACFT ON XWIND A FEW FT TO MY L AT ABOUT 100 FT ABOVE ME (THE PATTERN ALT IS 1200 FT MSL). I PUSHED THE CTL COLUMN FULL FORWARD AND DOVE FOR THE GND. THE SECOND ACFT PASSED OVERHEAD. THE SECOND ACFT DID NOT APPEAR TO TAKE ANY EVASIVE ACTION BUT THE PLT CLRLY SAW ME BECAUSE HE ASKED THE TWR TWICE WHAT I WAS DOING IN HIS AIRSPACE. AFTER THE SECOND INQUIRY; THE TWR CTLR TOLD HIM I WAS DEPARTING ON RWY 27. I DIDN'T SAY ANYTHING ON THE RADIO; NOT WANTING TO ADD TO WHAT WAS ALREADY A TENSE SIT. I CONTINUED MY CLB AND THE SECOND ACFT TURNED DOWNWIND AND CONTINUED WITH HIS PATTERN EXERCISES. WHEN MY DEST (N07) WAS IN SIGHT; THE TWR CTLR AUTH A FREQ CHANGE. THE REST OF MY FLT WAS UNEVENTFUL. THERE WAS NO DAMAGE TO EITHER ACFT.