A CL65 FLT CREW RECEIVE A TCASII RA AFTER THE D21 CTLR GAVE THEM A VECTOR.

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TOOK OFF ON RWY 3L IN DTW AT XA14Z. AFTER THE HDOF WAS RECEIVED; CREW CONTACTED DTW DEP CTL ON 125.52 AND WAS TOLD TO PROCEED DIRECT TO TYCOB INTXN AND CLB TO FL230. AT AROUND 10000 FT; THE CTLR TOLD US TO EXPEDITE THROUGH 13000 FT. WHILE PROCEEDING DIRECT TO TYCOB; THE CREW NOTICED AN AREA OF LEVEL 2 AND 3 WX AND ASKED THE CTLR FOR 5 DEG DEV TO THE L. THE CTLR IGNORED THE REQUEST AND TOLD US TO TURN R TO 180 DEG HDG. AT XA20Z IN IMC; THE CREW RECEIVED A TA FOR AN ACFT AT OUR 2 O'CLOCK POS AND HIGHER. THE CTLR TOLD US TO TURN R TO 230 DEG HDG. WITHIN SECONDS; WE RECEIVED AN RA FOR THE SAME TFC. THE TCASII RA TOLD US TO DSND. I (PF) IMMEDIATELY DISENGAGED THE AUTOPLT AND INITIATED A DSCNT. WE WERE CLRED OF THE CONFLICT AT APPROX 11500 FT. WE BELIEVE THAT THE INTRUDER ACFT WAS AT +2300 FT/-1000 FT OF OUR ALT AND APPROX 5 NM LATERALLY. AFTER REALIZING THE OCCURRENCE; THE CTLR TOLD US TO PROCEED DIRECT TO TYCOB AND THANKED US FOR THE HELP. THE FLT PROCEEDED SMOOTHLY TO HPN AND WAS SAFELY CONCLUDED.