PHOENIX » Judge G. Murray Snow pressed Sheriff Joe Arpaio to answer a bit of an odd question: Was the sheriff investigating the judge and his wife?

Snow had already ruled against Arpaio in a civil rights case brought by Latinos who said they had been singled out because of their ethnicity, and the sheriff was back in U.S. District Court here after admitting that he had violated an order barring his deputies from singling out Latinos they suspected of being in the country illegally.

But the issue at hand in late April involved whether Arpaio and the Maricopa County Sheriff’s Office had hired a rogue informant in Seattle — a compulsive gambler known for scamming federal agencies — to investigate whether Snow and the Justice Department were working together to take the sheriff down.

Arpaio testified that, yes, he had hired the informant. And that was only the half of it: Arpaio also said he had employed a private agent to investigate Snow’s wife after the sheriff received an email from someone claiming to have overheard her mention her husband’s negative views of the sheriff.

Both investigations led nowhere. But now, after Snow asked pointed questions about the dual inquiries — describing them as an effort "to construct some bogus explanation to subvert this court" — Arpaio’s lawyers are using the judge’s line of questioning to try to get the case reassigned. Arguing in court documents that Snow raised the specter of judicial bias and impropriety when he asked questions pertaining to personal matters in court, they are demanding someone new.

"This is not about vitriolic accusations against the judge — he’s a decent guy, a good judge," said A. Melvin McDonald, a criminal lawyer retained by Arpaio. "It’s about the personal animus he has displayed to the claim."

It is also a sign of how Arpaio has operated through much of his 22 years as sheriff, using his office and power to sidestep pressure to change his approach to policing, an issue that is part of the Justice Department’s lawsuit, filed in 2012. He had previously begun other investigations against critics and opponents, drumming up claims of corruption and other malfeasance against state judges, elected officials and the publishers of an alternative weekly, Phoenix New Times.

All of the cases eventually fell apart: Many of the accused successfully sued the Sheriff’s Office, earning millions of dollars in damages, paid with taxpayers’ money.

Snow now has to decide whether to remain on Arpaio’s case or to let another federal judge take his place.

Regardless, Arpaio has more legal troubles on the way: On Thursday, Judge Roslyn O. Silver, who is overseeing a civil rights lawsuit by the Justice Department against the sheriff and his office, ordered a bench trial to start Aug. 10.

An appointee of President George W. Bush, Snow has played referee and arbiter in the 7-year-old civil rights case against Arpaio since Judge Mary Murguma recused herself in 2009. Murguma’s recusal followed complaints from the sheriff about an appearance of conflict, given that her twin sister, Janet, was president and chief executive of the National Council of La Raza, one of the country’s largest Latino advocacy groups.

Snow ruled against Arpaio in May 2013, delivering what appeared to be a decisive blow against the six-term sheriff, then 80, a defining symbol of Arizona’s strict approach to immigration enforcement.

But 10 months later, Arpaio was back before him, facing stern reproach for defying his order to stop singling out Latinos during patrols and traffic stops.

He told Arpaio in April that he was looking for "a pattern that reflects a hesitancy on the sheriff’s office, on the sheriff’s department and on your part, or even a desire to subvert the orders of this court."

One of the issues involved the failure by Arpaio and his chief deputy, Jerry Sheridan, to properly disseminate the judge’s instructions to officers. Before the hearing, they admitted to this and other failings and pledged again to stick to the judge’s corrective measures.

But the hearing went on as planned.

In court in April, Snow noted that the Maricopa County Sheriff’s Office, also known as MCSO, was only 29 percent in compliance with the changes he had ordered 18 months earlier, right around the time the informant, Dennis Montgomery, started his investigation.

Snow said he was troubled — by both the investigation and what it had produced.

"The court wonders why, when the MCSO should have been spending their time, money and resources in implementing its order, they were funding a confidential informant as well as three MCSO deputies or posse members to be in Seattle, Wash., accruing overtime, travel and salary expenses, as well as significant technology costs, attempting to construct some bogus conspiracy theory to discredit this court," Snow said in court.

He took to referring to the investigation as the "Seattle Operation" and sounded skeptical when describing the reasoning and results of Montgomery’s work. He said Montgomery had "allegedly" used information "harvested by the CIA and confiscated by him" when he was a government software contractor.

The materials, the judge said, included fragments of email messages between the Justice Department and a former clerk of Snow’s, as well as snippets of phone calls Montgomery claimed to have tracked between Snow and the former attorney general, Eric H. Holder Jr., as well as with other high-ranking Justice Department officials.

On the stand, Sheridan said Montgomery had "pulled data from American citizens for the CIA," an assertion the agency has denied.

When Snow suggested that the materials provided by Montgomery were "junk," Sheridan and Arpaio agreed.

But the tale of the conspiracy has nonetheless reverberated from the glass-and-steel Sandra Day O’Connor U.S. Courthouse here to the halls of the Justice Department and the Pentagon. Last month, Snow asked Michele M. Iafrate, who is representing Arpaio in the civil contempt case, to write to the CIA, informing it that her client may be in possession of some of its materials.

The cache is also said to include bank account numbers and balances for about 50,000 residents of Maricopa County, Sheridan told Snow.

Montgomery, however, could just be bluffing: His reputation, easily uncovered with a cursory search, includes ample evidence of deception. He duped the federal government more than once, according to federal officials, selling it anti-terrorism technology that proved to be a hoax.

In 2007, he falsely accused the governor of Nevada at the time, Jim Gibbons, of having received kickbacks from Montgomery’s former employer to help it secure secret federal defense contracts. Two years later, Montgomery was arrested on charges that he had written $1 million in bad checks at a Las Vegas casino. He filed for personal bankruptcy that year, over mounting gambling debts.

"This guy hired a person previously found to be a con man," said Dan Pochoda, senior counsel for the American Civil Liberties Union of Arizona, which represents the plaintiffs in the case against Arpaio.

The sheriff’s office certified Montgomery as a confidential informant. On the stand, Arpaio said he did not recall how much money Montgomery had gotten for his work.

Stephen Lemons, the Phoenix New Times columnist who first reported the link between Montgomery and Arpaio, said he had relied on information from "longtime sources," including a former detective in the sheriff’s Special Investigations Division, the unit that had been handling Montgomery.

On Jan. 21, Lemons wrote about the investigation into Snow’s wife. It started, the article said, after a sympathizer wrote a private Facebook message to Arpaio, telling him that the judge’s wife, an old acquaintance, had mentioned during a casual encounter at a Mexican restaurant that the judge was out to get him.

Larry Klayman, Montgomery’s lawyer, a well-known defender of conservative causes, has mostly taken aim at Lemons, calling him a "sleazy reporter" working for a "discredited, ultraleftist and pro-illegal immigrant" publication.

But when questioned by Snow in court, Arpaio and Sheridan confirmed what the judge had highlighted: The investigations described in Lemons’ reporting were real.