DEPARTING PA31 AND ARRIVING CARJ EXPERIENCE NMAC NEAR TVC AFTER TWR IS CLOSED.

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AFTER DROPPING OFF PAX WE DID AN IMMEDIATE TURN AROUND. THE TWR HAD BEEN CLOSED FOR SOME TIME AND THEY FAILED TO SWITCH THE ATIS OVER TO THE AUTOMATED BROADCAST. IN VIEW OF THIS; WE DECIDED TO TAXI OVER TO THE WIND SOCK. THE WINDS; ALTHOUGH LIGHT; FAVORED RWYS 18 AND 28. THE OUTDATED ATIS HAD THE WINDS FAVORING RWYS 36 AND 10. SINCE WE NEEDED TO DEPART TO THE S AND SEVERAL ACFT COULD BE SEEN ON FINAL FOR RWY 10 WE ELECTED TO DEPART ON RWY 18. WE CONTACTED ZMP AND RECEIVED OUR CLRNC. SEVERAL MINS LATER; WE RECEIVED AN OVERVIEW OF ARPT TFC AND WERE RELEASED FOR TKOF. BEFORE THE TKOF ROLL BEGAN; WE SWITCHED TO ADVISORY FREQ AND ANNOUNCED OUR INTENTIONS. WITH SAFETY IN MIND; WE ROTATED WELL BEFORE INTERSECTING RWY 10. ALTHOUGH WE WERE GIVEN AN OVERVIEW OF TFC; WE ONLY ACKNOWLEDGED THAT WE HAD THE TFC OUT TO THE W IN SIGHT. THIS WAS ALL WE COULD VIEW DUE TO THE ARPT LAYOUT. UPON REACHING ABOUT 2000 FT MSL; WE CONTACTED ZMP ONCE AGAIN. ZMP RESPONDED 'ROGER RADAR CONTACT; CLB AND MAINTAIN 8000 FT.' THE CLB WAS CONTINUED AND ABOUT 20 SECONDS LATER A REGIONAL JET CROSSED FROM L TO R VERY; VERY CLOSE. I STOPPED THE CLB. AFTER A FEW SECONDS; I WAS ABLE TO INQUIRE TO ZMP ABOUT THE INCIDENT. THEY TRIED CONTACTING THE REGIONAL JET BUT THEY HAD BEEN ON ADVISORY FREQ. 3 MINS LATER; THE REGIONAL JET; THEN ON THE GND; STARTED INQUIRING ABOUT THE INCIDENT. ZMP CTLR TOLD THEM HE THOUGHT THE PA31 HAD THEM IN SIGHT; AND HE APOLOGIZED. THEY REPLIED THEY HAD INITIATED A 3000 FPM TCAS CLB TO AVOID US. IN THE FUTURE; I WILL LEAVE THE WINGTIP LNDG LIGHTS ON TILL I REACH CRUISE ALT AND MAKE AN EXTRA POINT TO CHK MY BLIND SPOTS. MY SENSE OF COMFORT FROM THE WORDS RADAR CONTACT WILL NEVER BE AS GREAT.