PC12 First Officer reported Autopilot failure resulted in a steep descent and altitude deviation below assigned altitude.

Narrative

On Day 0; flight from ZZZ1 to ZZZ while flying Aircraft X between the hours of XA20 - XB10; the Autopilot of the aircraft over corrected and started a rapid descent. Weather conditions: light to moderate rain and turbulence. My Captain was pilot monitoring (PM) and I was pilot flying (PF). ZZZ Approach Control descent us from 4000 ft. to 3000 ft. SOPs were followed during the descent and I initiated a stabilized vertical descent of 1000 FPM with the Autopilot engaged. My Captain requested I increased the descent rate to 1500 FPM and I complied with his request. My left hand was on the yoke and right hand was on the power control lever because of weather conditions and I was prepared for the Autopilot to disengage which it didn't. We kept the airspeed below 200 kts. on descent. My hand felt heavy and VSI started to increase along with supported instruments and I said 'this is too steep' and my Captain took controls disconnected the Autopilot and we reduced the power to idle and pulled up. At that time we regained control of the aircraft at 2200 ft.; sink rate was announced and the controller said to check our altitude. My Captain requested a heading and altitude from the controller just so we can gain situational awareness and assess what went wrong. There was no wind shear reported; no aural warning for trim runaway and no pusher CAWS. He double checked my entry into the Autopilot system just to make sure I didn't put more than what I was told. After realizing it wasn't a pilot error; we requested vectors for final for RNAV GPS Y XX at ZZZ. We landed safely and grounded the aircraft.