LGT IN CLB HAD NMAC WITH VFR COMMUTER.

Narrative

AFTER TKOF FROM RWY 4; LGA; DEP CTL GAVE US A 270 DEG HDG AND CLRNC TO CLB TO 15000 FT. TFC WAS VERY LIGHT; WX WAS CLR; VISIBILITY UNLIMITED. PASSING APPROX 8800 FT ESTABLISHED IN OUR CLB; 250 KTS; AT 2500 FPM; WE RECEIVED A TCASII TA FOLLOWED IMMEDIATELY BY AN RA COMMANDING A MIN DSCNT RATE OF 2500 FPM. THE TCASII HAD BEEN SET TO THE 10 MI SCALE AND INDICATED TFC CENTERED WITH NO HORIZ SEPARATION. INITIATED PUSHOVER AND REACHED APPROX 9300 FT BEFORE PASSING THROUGH LEVEL FLT. AT THAT POINT DEP CALLED OUT VFR TFC; 12 O'CLOCK; NBOUND AT 9500 FT. TCASII STILL INDICATED NO SEPARATION. NEVER SAW TFC -- APPARENTLY WAS DIRECTLY OVERHEAD. TCASII THEN INDICATED CLR OF TFC. IN RETROSPECT; ATC TFC WAS SO LIGHT THAT I REMEMBERED A COMMUTER CANCELLING IFR AND GOING VFR TO ALBANY. HE HAD BEEN CLRED VFR AT 9500. DEP CTL; AT THAT POINT; CEASED PROVIDING SEPARATION FROM US. WE WERE GIVEN A VECTOR AND CLB CLRNC WHICH PUT US ON A PERFECT CONFLICT IN BOTH POS AND ALT. I FEEL VERY FORTUNATE TO HAVE BEEN IN A TCASII EQUIPPED ACFT. DEP CTL'S CALL AT THAT POINT WAS IRRELEVANT. ATC KNEW HIS ALT. ALTHOUGH POSSIBLY LEGAL; DEP CTL WAS REMISS; ESPECIALLY GIVEN THE VERY LIGHT WORKLOAD. CONCERNING HUMAN PERFORMANCE: I HAD NEVER ANTICIPATED A TCASII RA COMMANDING SUCH A VERY LARGE CORRECTION. THE VERT SPD DIFFERENCE BTWN ACTUAL AND COMMANDED WAS OVER 5000 FPM. I INITIALLY WAS AFRAID OF CLBING THROUGH HIS ALT BEFORE PASSING THROUGH IT ON THE WAY DOWN (BEFORE ATC CALLED HIS ALT). THE PUSHOVER WAS STARTED BEFORE ATC CALLED; HOWEVER. THE WX WAS SO OUTSTANDING; SMOOTH; EXCELLENT VISIBILITY; AND QUIET RADIO; WE WERE ALL ENJOYING THE SCENERY. THE TCASII BROKE THE SILENCE AND QUITE FRANKLY; CAUGHT US BY SURPRISE -- ESPECIALLY THE DEG OF CORRECTION NEEDED. IT IS NOT NATURAL FOR US TO MAKE LARGE ALT DEVS IMMEDIATELY FROM A 'NEWCOMER' IN THE COCKPIT. ALTHOUGH I FOLLOWED THE COMMAND; I WILL IN THE FUTURE MAKE IT A POINT TO REACT EVEN FASTER WITH MORE AUTHORITY. FROM WATCHING KNOWN TFC ON TCASII; I HAVE KNOWN THAT IT IS VERY ACCURATE. THIS RPT IS SUBMITTED DUE TO INADEQUATE TFC SEPARATION AND THE PERFORMANCE OF THE TCASII SYS. NO CLRNC DEV OCCURRED.