A Deed of Trust state would be non-judicial since the trustee listed on the Deed of Trust actually forecloses on the instrument where a Mortgage state, judicial, has to go through the courts to be foreclosed on. 

Now we do report foreclosed on Deed of Trust and Mortgages as an open security instruments unless there is an actual Release or Satisfaction filed with the Recorder's office.  It is just what we do and let the client strike it off.