Gov. Charlie Baker and Attorney General Maura Healey have both launched probes into why a state trooper was ordered to scrub embarrassing details about the arrest of a judge’s daughter from his report, with Baker promising a speedy conclusion to what he dubbed a “significant” investigation.

The spotlight on the October drug and OUI arrest of Alli Bibaud — the daughter of Dudley District Court Judge Timothy Bibaud — comes as trooper Ryan Sceviour’s lawyer promised to depose state police Col. Richard McKeon and other top officials under oath in the trooper’s federal lawsuit.

Leonard Kesten, Sceviour’s attorney, said last night on WRKO’s “Howie Carr Show” he also intends to file a lawsuit on behalf of trooper Ali Rei, who administered drug tests to Alli Bibaud and was ordered to shred her notes.

“She was given one paper copy while she prepared her report, with an order to shred when she was done,” Kesten said, adding that Rei refused to do so. “She has been very afraid of retaliation.”

Baker said yesterday of his Public Safety Secretary Daniel Bennett, a former Worcester prosecutor, “incontrovertibly … was not” involved in the matter. Baker promised a “significant review” and said he won’t take any action until it is complete.

“Those are serious allegations. It’s very important that the facts associated with them be properly vetted. People want us to take these things seriously. You don’t take something seriously in 24 hours, OK?” Baker said.

Healey said yesterday her office also is “reviewing” the allegations.

“The allegations are concerning,” Healey said, declining to comment further.

Sceviour’s lawsuit says he responded on Oct. 16 to a car crash on Interstate 190 in Worcester and arrested Alli Bibaud, 30, after she failed field sobriety tests and was found to have a heroin kit in the car, the lawsuit said. Sceviour said Bibaud told police her father was a judge, that she had performed sex acts to obtain the drugs, and suggested “she would offer sexual favors in return for leniency.”

Days after he wrote the report, his federal lawsuit states, Sceviour was awakened at his home by a trooper and ordered to drive to the barracks to edit out the woman’s embarrassing statements.

State police spokesman David Procopio has defended the orders to edit the report, saying it was intended to remove “sensationalistic” statements and claiming that such revisions are common. Sceviour has disputed that claim, and Kesten dismissed the explanation as “laughable.”

That was pretty much the same tack taken by the Worcester DA’s office. Prosecutor Jeffrey Travers went before a Worcester District Court judge four days after Bibaud’s arrest and sought to redact Bibaud’s statements from the police report because they were “purely prejudicial to the defendant.”

“The commonwealth is suggesting the redactions, which I’ve handed up, are appropriate given the commonwealth’s ethical obligations to avoid unnecessary pretrial publicity with respect to the defendant,” Travers told the judge.

“I suggest to you the statements are extraneous to anything in reply to the finding of probable cause and really are purely prejudicial to the defendant,” he said.

The judge allowed the redactions.

Worcester District Attorney Joseph Early Jr. refused to comment yesterday.

A trial court spokeswoman has said the judiciary “has no information” that Judge Bibaud was involved. Bibaud could not be reached for comment.

At the State House yesterday, McKeon left the building through an emergency exit followed by reporters, telling them, “I know the allegations are directed at me. I have no comment about it at this time.”

Kesten said he is scheduling the first depositions for the second week of December, starting with the trooper’s immediate superiors, including Maj. Susan Anderson.

“We’ll just keep going,” Kesten said. “I don’t want to get to the colonel until I have records.”