BE35 DEPARTING IFR FROM CWA IN A NO RADAR ENVIRONMENT HAS NMAC WITH AN INBOUND C172.

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I WAS CLRED INTO POS ON RWY 17. I OVERHEARD A CESSNA TELL CWA TWR THAT HE WAS 5 MI SE AT 3000 FT. TWR CLRED ME FOR TKOF; L TURN ON COURSE (125 DEGS). MY IFR CLRNC WAS 'AS FILED (DIRECT KOOKY; MKG; AZO); MAINTAIN 4000 FT; EXPECT 9000 FT 10 MINS AFTER DEP; CONTACT ZMP ON 124.4....' AFTER TKOF; I TURNED L TO 125 DEGS AND WAS ADVISED TO CONTACT ZMP. AS I CLBED OUT; I SUDDENLY SAW THE CESSNA PASSING JUST ABOVE AND BEHIND MY L WING. I WAS AT 2900 FT AND CLBING. HAD I STARTED MY TKOF ROLL 5 OR 10 SECONDS EARLIER; WE WOULD HAVE COLLIDED. I WENT BACK TO THE TWR FREQ AND RPTED THE NMAC. THE CESSNA PLT ALSO TOLD THE TWR HE HAD SEEN ME PASSING BEHIND HIM; TOO LATE FOR ANY EVASIVE ACTION. I THEN HEARD THE TWR CTLR ATTEMPTING TO CLARIFY THE CESSNA'S POS ON THE EARLIER CALL. THE CTLR SAID HE HAD THOUGHT THE CESSNA WAS '5 MI S' BUT THE CESSNA PLT MAINTAINED HE RPTED '5 MI SE.' IN RETROSPECT; I SHOULD HAVE QUESTIONED THE CTLR ABOUT A POSSIBLE TFC CONFLICT BEFORE ACCEPTING THE TKOF CLRNC. IT SHOULD BE NOTED THAT CWA TWR DOES NOT HAVE RADAR AND CTR RADAR DOES NOT EXTEND BELOW 4000 FT IN THIS AREA. ZMP WAS NOT TALKING TO THE CESSNA; WAS NOT AWARE OF THE NMAC; AND I RPTED IT ONLY TO CWA TWR.