Challenger 300
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 55; Flight Crew Total 5900; Flight Crew Type 370
Conflict Airborne Conflict; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Hazardous Material Violation; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Flight Crew Took Evasive Action; Flight Crew FLC complied w / Automation / Advisory
Human Factors; Procedure
ATC gave us a descent to FL340 while in a left hand turn from a heading of 170 to 330.  At roughly FL355; we received a TA on an aircraft left of our nose that we did not see and was not yet called out by ATC.  We queried ATC about the TA traffic and as ATC gave us information; we received an RA of 'adjust vertical speed'.  As Pilot Flying; I followed the RA commands in the cockpit and reduced our rate of descent and then visually acquired the traffic.  Once we received the 'clear of conflict' audio; I lowered the flight deck angle in order to continue descent while maintaining visual of the traffic.  I received an alert that I was 300 feet below our pre-selected altitude and quickly arrested the descent and climbed back to FL340.  Our cockpit indication was that we descended to FL335 at the low point before recovering back to FL340.  ATC contacted us and gave us the phone number to call.  After landing; we contacted ATC and they informed us that there was a 'loss of separation' of 800 feet and 3 nautical miles.  ATC's threshold is 1000 feet and 5 nautical miles.  We discussed the events that took place in the cockpit.  I informed ATC of our failure to level off at the assigned altitude after reacting to the RA and that both pilots were scanning outside the cockpit to gain a visual on the traffic.  We recognized our deficiency in maintaining an outside and inside scan throughout this evolution.  In the near term; we will brief our team and review the Pilot Flying and Pilot Monitoring duties and responsibilities when searching for traffic; reacting to RA's and when we are within 1000 feet of planned level off.
The secondary narrative contained no additional information.
While in a descent; cleared to FL330; the flight crew of a CL30 responded as directed to a TCAS TA followed shortly by an RA. Upon completion of the avoidance maneuver they continued their descent while monitoring the traffic visually. While doing so they inadvertently descended approximately 500 feet below their cleared altitude.