Flight crew flying CL350 aircraft reported uncommanded rudder trim during climb out. Flight crew diverted and returned to departure airport.

Narrative

The departure runway was XXL. We were assigned the departure. Our initial altitude was assigned to be 11;000 (climb via). The highest altitude we reached was 5;000 before broke off the departure. All occurrences leading up to the event were normal. At proximate 700 feet AGL the rudder trim went all the way to the right position. The aircraft was being hand flown (autopilot disengaged) at the time this occurred. The Captain; who was pilot flying; selected three incremental activation's of the rudder trim switch to the right side. The trim; according to his account; continued to operate without his selection to the full right hand side position. I; as pilot monitoring; was completing the after takeoff checklist and did not see the Captain select the trim switch to accommodate the position he requested. I felt a yawing motion to the right hand side and saw that the rudder trim indicator indicated a full right position. The captain stated that he selected the switch on his control column; which is a memory item. I re-centered the trim switch because the Captain had full left rudder pedal in to counteract the trim position. I was not aware the trim had moved to its position without being commanded. I was not sure if it was inadvertent. The Captain then stated he did not select the position. At this time I asked ZZZ Departure control to level and advised them we needed to return. We were given an assigned heading for vectors back in. Captain called for autopilot on to which I selected autopilot on in HDG and VS modes. Several seconds after I selected autopilot on the trim began to move to the right without being commanded to do so. The Captain immediately activated the switch which stopped the trim from moving immediately. The trim remained in that position for the rest of the flight. Neither I nor the Captain attempted to move the rudder trim again and the switch was untouched for the rest of the flight.ATC [requested priority] on our behalf as we were busy flying the plane and making sure the aircraft was appropriately configured for a return to ZZZ on Runway XXL. The Captain and I accomplished the memory items associated with the event; the only memory item associated with the event was that the pilot flying activate the MSW to stop the trim movement. The decision was made that we needed to return immediately as the aircraft was in a controllable state instead of finishing the checklist. As the checklist items that remained on the pertinent checklist that we did not do would have not altered the result because the trim motion stopped when the captain selected the MSW which was part of the checklist. I looked at the appropriate checklist but we did not want the aircraft to digress into an uncontrollable state so at that time I told ZZZ approach that we were ready to commence a visual approach at the Captains request. He stated we needed to return immediately instead of prolonging our time airborne; I agreed. The Captain hand flew the aircraft (autopilot disengaged) for the remainder of the flight. We commenced a visual approach to Runway XXL at ZZZ and landed without incident. We taxied off the runway; assistance was not required. We continued to taxi to the ramp and shutdown the airplane.