Lawyers sparring over a Wisconsin man accused of killing his three daughters bobbed and jabbed Thursday while he sat still as stone.

If Aaron Schaffhausen was interested in the outcome, he didn't show it, muttering a nearly inaudible answer when Judge Howard Cameron asked him if he agreed to a plea of not guilty by insanity.

With that, Schaffhausen's forthcoming trial in St. Croix County Circuit Court -- already commanding wide public interest in two states -- took on a new dimension that could involve much more expert testimony and a flurry of new motions in a two-part trial before the same jury.

"It adds more witnesses, and it adds more challenges for everyone," prosecutor Gary Freyberg said after the hearing.

Schaffhausen, then a 34-year-old construction worker, was charged July 12 with three counts of first-degree intentional homicide in the throat-slashing deaths of his daughters Amara, 11; Sophie, 8, and Cecilia, 5. He's accused of killing them in the River Falls, Wis., house they shared with their mother, Jessica Schaffhausen, his former wife.

Although irritated that defense attorney John Kucinski had missed a deadline for filing an insanity plea by more than a month, Cameron accepted it and said he would issue an order that allowed the prosecution to conduct psychological examinations of Schaffhausen.

The plea was entered Wednesday in a one-paragraph letter from Kucinski, an assistant public defender in Wisconsin. Cameron had set a Dec. 14 deadline, and Freyberg had expressed concern that a psychological exam could take three months.

Schaffhausen's trial is scheduled to begin April 1.

The hearing also covered other legal territory, with Cameron denying defense motions to move Schaffhausen's trial out of Hudson, Wis., and to suppress statements Schaffhausen had made after his arrest. On a third matter, Cameron said he would consider a defense motion to ban cameras from the courtroom during the trial -- but he didn't sound sympathetic.

"It's basically just factual reporting," Cameron said, explaining that he had reviewed newspaper stories and broadcast reporting of the case and hadn't found any inaccuracies.

Schaffhausen's plea sets up a two-phase trial, the first to determine whether Schaffhausen committed the crimes, then one to determine his state of mind and whether he's not guilty by reason of insanity.

At times in Thursday's hearing, Kucinski and Freyberg argued over who should conduct psychological examinations and how the findings would be shared. Both attorneys swung into arguments over evidence, expert witnesses and timing.

Their strongest disagreements came when Freyberg said he was entitled to notes taken by defense experts when they examined Schaffhausen. "Unless we have those, our experts will be unable to examine the defendant properly," Freyberg said.

Kucinski objected that he wasn't compelled by law to do so. He said outside the courtroom after the hearing: "Experts are supposed to be independent, are they not? In no cases do other people turn over to another expert their report. That's unheard of."

He also said he had filed Wednesday's insanity plea "out of frustration" because of court-imposed deadlines.

Freyberg said after the hearing that he was concerned by what he saw as delays and dodges by the defense. "A trial is supposed to be a search for the truth," he said.

The insanity plea can be withdrawn before trial. Should that happen, psychological evaluations supporting the plea would not be admissible.

Schaffhausen pleaded not guilty "by reason of mental disease and defect to all four counts" -- three counts of first-degree intentional homicide and one of attempted arson. Authorities at the crime scene found a fireplace turned on and gasoline poured in the basement.

According to a criminal complaint, Schaffhausen had been a carpenter living in Minot, N.D., when he asked his ex-wife about noon on July 10 to spend time with the children.

She agreed but told him he had to leave the house by 3:30 p.m., before she got home, the complaint said. A baby sitter said the girls were excited to see him and led him upstairs to their bedrooms.

The sitter left, and at 3:30, Jessica Schaffhausen told police, her ex-husband called to say he had killed the children. Police found them in their beds with blankets pulled to their chins. Two had their throats slit. The third girl was strangled and had cuts on her neck.

Schaffhausen will next appear in court on Jan. 31, when Cameron hears motions on the exchange of mental health records.

Kevin Giles • 651-925-5037 Twitter: @stribgiles