Baugh, 72, has apologized for his handling of the case and plans to retire at the end of the year.
He said Tuesday he had not yet seen the complaint and could not comment on it.
The commission is alleging that Baugh's statements about the victim were inconsistent with a state law that requires child rape victims to be evaluated based only on their age — not on a "subjective" judgment of their physical maturity or control of the situation.
The complaint also charges that the prison sentence given to rapist Stacey Rambold was "overly lenient" and illegal under state law. Baugh sentenced the former teacher to 15 years in prison with all but one month suspended barring further violations.
Prosecutors have appealed, saying Rambold should have received a mandatory minimum of four years in prison.
Rambold's response to the appeal is due at the end of the month. The former Billings Senior High School business teacher was released from prison in September and remains free pending the appeal.
In a November letter to the commission, Baugh acknowledged that his actions during Rambold's August sentencing hearing had eroded confidence in the courts. He later told The Associated Press that he deserved to be censured but not removed.
His comments sparked international outrage and hundreds of complaints to the judicial commission, including from the Montana chapter of the National Organization for Women.
Advocates from that organization and others have called for Baugh to resign or be removed by the Supreme Court.
Commission attorney Malin Stearns Johnson said details on proposals for disciplinary action typically are filed with the court at a later date.
Sheena Rice, with the Montana Organizing Project, helped arrange an August rally outside Baugh's courthouse that drew several hundred. She said Tuesday she still hoped to see Baugh resign and was glad that the judicial commission was taking action.
"It's been a long road since the end of August, but it's good to see something come out of what we did," Rice said.