Flight crew reported smoke in the cockpit after landing and requested Airport Rescue and Firefighting (ARFF) to meet the aircraft on the taxiway and ran the QRH. The smoke dissipated and ARFF found no evidence of fire.

Narrative

I was the First Officer assigned to work Aircraft X from ZZZ1 to ZZZ on Date. I was pilot flying (PF) for this flight with the Captain pilot monitoring (PM). During the flight from takeoff to landing nothing abnormal happened and the inflight portion concluded with a normal landing to Runway XXR in ZZZ. After clearing the runway at Taxiway XX we were assigned by ground to continue taxing to the ramp area via XY. The captain made the turn on to XY. At this time I noticed smoke begin to emit from the air vents on both my side of the cockpit and the Captain's side. We both asked out loud if this was smoke and immediately smelled smoke in the air. The Captain instructed me to call the cabin and ask the Flight Attendants if they could see and or smell smoke. The cabin crew however called up instantly to state there was smoke in the cabin to which I said to the Captain 'they have smoke in the cabin'. The Captain stated he was going to stop the aircraft on XY and for me to tell Ground as well as have them send out the fire trucks. I made the call to Ground and the fire trucks were sent out. At this time the Captain called for the smoke; fire; fumes QRC. We began to accomplish the checklist from the card and then I transitioned to the iPad. Halfway through the checklist the cabin crew called and said a passenger saw smoke exiting from the right engine; to which the Captain instructed I shut down the right engine. We did not have any fire warnings illuminated. However it should be noted that we did not know where the smoke was coming from and were trying to safety eliminate possible sources as directed by checklist as well as from information coming from the cabin. After shutting down the engine we continued to run the checklist; which had us shut off both PACKs; the recirculation fans; utility buses; and APU bleed. During this time the smoke had not increased and was beginning to dissipate. We briefly discussed that at this time an evacuation did not seem needed and I agreed. At this time the fire department arrived and stated that our brakes and engines appeared to be within normal range and it appeared we would be safe to taxi. We agreed an evacuation was not required. We requested the fire trucks follow us to the gate and we taxied to the gate without incident. Upon arriving at the gate we informed Operations and Maintenance of what had occurred.