Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 190; Flight Crew Total 17000; Flight Crew Type 3000
Conflict NMAC
Air Traffic Control Issued New Clearance; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Took Evasive Action
Procedure
AT 7000 feet on MILTON STAR we were cleared to descend to 3000.  We began descent and were told to turn left 15 degrees.  We saw a target on TCAS and visually confirmed we were turning and descending away from the target.  The traffic triggered a descend RA.  The first officer flew the procedure per SOP which matched what we were already cleared to do.  We did not have to deviate from our clearance.  We continued with an uneventful landing at LGA.
Got a TCAS TA and while visually looking for traffic we received clearance to descend to 3000 feet.  We began descent then we were given 'turn left 15 degrees' by ATC. Received TCAS 'descend' RA and I expedited descent and followed commands on PFD. I saw the aircraft passing by our right wing and approximately 400 above us.
A B737 inbound to LGA on the MILTON STAR suffered an NMAC with an unidentified aircraft while complying with an ATC clearance followed by TCAS TA and RA alerts.