EMB-190 pilot reported refusing an aircraft that required excessive trim to fly stable. Maintenance was unable to address the trim issue to the satisfaction of the flight crew and the aircraft was removed from service.

Narrative

Upon arrival at the gate in ZZZ; the Check Airman operating the inbound flight informed us that the aircraft required 'more rudder trim than I've ever seen' to keep the slip-skid indicator centered in all phases of flight. I found another write-up a few weeks prior for the same issue. In my discussions with Maintenance Control; I tried to ascertain whether there was a published limit for required rudder trim from Embraer and if so; what it was. I was given multiple different answers; ranging from 'one unit' (there are no units on the E190 rudder trim indicator) to '2.4 degrees' (there are no degrees either); and nobody could tell me what any of these would correlate to in terms of what I could actually see on my Primary Flight Display (PFD). The Maintenance Control Technician then instructed our Mechanic to pressurize the hydraulics; center the rudder trim and verify that the rudder was centered; which it was. The Technician then performed the 'Return To Service' Self-Test on the rudder system; which seemed to pass (although the Technician did not clearly communicate what the Mechanic needed to see from this read-out; so he was unsure that this was the case). All of this led us to believe that the rudder was; in fact; working properly; and that there was likely another issue with the aircraft causing it to fly crooked. In the hours that followed; our Mechanic had several phone calls with Maintenance Control.On the last of these; I overheard the Technician stating that 'this thing has been on the ground long enough' at least three separate times. It was at this point that Maintenance Control decided to apply MEL 27-XX-XX on EICAS. This made no sense; considering we had already verified the proper function of the rudder and yaw trim system; both visually and with the self-test. When I pressed the Technician further on what was actually causing the aircraft to require so much rudder trim in flight; the Technician said: 'I have no idea'. It was at this time that my First Officer and I decided that we could not accept the aircraft without additional corrective action. We advised the Duty Chief of the situation and our decision. Our Chief's concern was that; in the event of an engine failure or another non-normal requiring significant rudder; we may not have the control authority to safely fly the aircraft. It should be noted that the local Mechanic expressed his discomfort with the situation as well stating: 'I don't want my name on that.'