ACR CLBING TO ASSIGNED ALT HAS TCASII TA THEN RA. RESPONDS.

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TCASII GAVE TA. I NOTED THE TFC ON THE TCASII SCREEN AT 10 O'CLOCK AND +800 FT; THEN I NOTED THE TFC VISUALLY. NEXT; TCASII GAVE AN RA WITH VERBAL 'DSND' INSTRUCTION. AT THIS POINT THE TFC I SAW DID NOT APPEAR TO BE A PROBLEM TO US. THEN; HARTFORD DEP CALLED THE TFC TO US AND INSTRUCTED US TO TURN TO A 160 DEG HDG. THE TURN WOULD CAUSE MORE OF A CONFLICT BY MY PERCEPTION SO I TOOK THE AIRPLANE AND DSNDED WHILE MAKING THE TURN. WE ADVISED DEP OF THE TCASII RA AND THE DSCNT. DEP GAVE US A FREQ CHANGE TO BOSTON CENTER AND ADVISED US OF VFR TFC AT 8500 FT IN OUR GENERAL DIRECTION OF FLT. THIS CAUSED CONFUSION AT A BUSY TIME -- CHANGE OF FREQ WAS NOT A GOOD IDEA AT THIS TIME; BUT WE CHANGED FREQ. WE DSNDED FROM APPROX 9800 FT TO APPROX 9400 FT WHILE THE CONFLICT WAS RESOLVED. WE NEVER SAW AND TCASII NEVER RPTED THE SECOND TFC. TCASII SEEMED TO WORK AS IT SHOULD EXCEPT THAT A LEVEL OFF SHOULD HAVE RESOLVED THE CONFLICT AND TCASII VERBALLY CALLED FOR A DSCNT. NO GREEN LIGHTS WERE NOTED. HARTFORD DEP AND BOSTON CENTER; IT WOULD SEEM; COULD HAVE COORDINATED THE TFC AND US BETTER. THEY CERTAINLY COULD HAVE BEEN MORE CLR ABOUT THE TFC AND COULD HAVE AVOIDED A FREQ CHANGE DURING TCASII RESOLUTION.