Babeu's former lover was an immigrant from Mexico who other news outlets have identified as Jose Orozco. Both men have said publicly in recent days that Orozco was in the United States legally.
However, there is some evidence to suggest that might not be true.
Orozco appeared on CNN this week, and the network said he told them he was in Arizona on a "10-year, US tourist visa that allows multiple crossings at the border."
But as the Arizona Daily Star first noted, US tourist visas generally allow foreign visitors to be in the country for no more than six months at a time. The visas may not expire for a decade, but that doesn't mean the person is allowed to stay in the United States for more than half a year at a time.
That could be problematic for Orozco, who previously told the Phoenix New Times that he began dating the sheriff in 2006. And it could be equally troublesome for Babeu, who told CNN that he and the man dated for three years.
Prominent immigration attorney David Leopold, who has practiced in Ohio for about 20 years, told TPM that it's highly unlikely that immigration authorities would have allowed Orozco to stay in the United States with a tourist visa for three to six years.
He said it's possible Orozco could have stayed for six months, returned to Mexico for a brief time and then asked US immigration authorities to let him come back for another six month stay. But he wouldn't be able to carry that on for years.
"They are probably going to let him do that once or twice," Leopold said. "But on a (tourist visa), the applicant is making a representation to the United States government that he is visiting. So they may let him do this once, maybe twice. But eventually they're going to say, you know, man, you're not living in Mexico."
Orozco's legal status is important. In his original interview with the Phoenix New Times, he accused the sheriff of threatening to have him deported if their relationship ever became public. The newspaper granted partial anonymity to Orozco at the time, calling him by only his first name and blurring out his face in a photograph of him and Babeu together.
His allegations, combined with the anonymity, raise the question of whether he may have known about these potential problems with his immigration status. The story also said he hired an immigration attorney to help him deal with the alleged threats.
His status is also important because of Babeu's role as a border hawk. Since being elected sheriff in 2008, Babeu has become a rising Republican star because he was one of the most vocal critics of illegal immigration in the nation, regularly bashing the federal government for what he described as a failure to secure the US-Mexico border.
Orozco's attorney, Melissa Weiss-Riner, did not respond to TPM's multiple requests for comment. Likewise, neither Babeu nor his campaign manager Chris DeRose returned calls seeking comment.
The sheriff told Phoenix radio station KFYI this week that he was sure his former boyfriend's immigration documents were in order.
"He's not illegal," Babeu said. "He's here legally. I've always said that. He's said that. In fact, his lawyer has said that."
Yet Leopold, the immediate past president of the American Immigration Lawyers Association, said there's plenty of reason to believe that's not true, given what both men have said to other media outlets in recent days.
"Bottom line is there is no way he had authorization to be here for 10 years. I can tell you that right now," Leopold said. Even if Orozco was granted a six month extension of his original stay, the timing puts him well past that deadline. "That would mean that the visa that he's got in his passport is going to be invalid, since he overstayed."
Kevin Johnson, the dean of the UC Davis School of Law, agreed that the men's statements raise questions about Orozco's legal status.
"He may have overstayed his visa and be undocumented," Johnson said in an email to TPM. "It would be hard to say without lots more facts, however."
Leopold said this is where the sheriff could face other legal problems.
According to US law, it's a crime to knowingly harbor an undocumented immigrant. A strict reading of the law, Leopold said, would include some of the typical things that couples do, like driving together in a car.
Most of the time, authorities wouldn't prosecute the boyfriend or girlfriend of someone who has problems with his or her immigration status. But in this case, Babeu is in a position of law enforcement, someone trained to know better. Moreover, he has made a career out of being a hardliner on the subject. A prosecutor and judge would likely hold the sheriff to a higher standard, Leopold said.
"I think the sheriff's got a problem if that's what was going on. He's got a big problem," Leopold said. "If they indicted him and charged him, there might be some meat to it."
It's possible that Babeu could say that the subject never came up or that he was fooled by his ex-boyfriend. But even that might be a hard sell, given Babeu's expertise on immigration matters and his role as an investigator.
Plus, Leopold said, the subject almost always comes up.
"Based on my experience with families with people that don't have documents, it comes up pretty quickly," he said. "It's rare that it doesn't. And especially if you're involved in an intimate relationship."
Meanwhile, Arizona's top prosecutor said he is going to investigate the possible crimes on both sides. Attorney General Tom Horne's spokeswoman confirmed to TPM that he plans to look at the scandal.
Like Babeu, Horne is a hardliner against illegal immigration and vocal supporter of the state's harsh immigration law, which was designed to force state and local police to have a greater role in immigration enforcement.
Horne and Babeu have also been political allies. During his 2010 run for attorney general, Horne received the sheriff's endorsement.
Horne took up the investigation after the sheriff and top prosecutor in Arizona's tiny Gila County refused to look into the matter. On Tuesday, Babeu had asked the Gila authorities to take the case, saying he wanted independent investigators to look into his former boyfriend as well as the allegation that the sheriff threatened to have him deported.
Babeu has accused his former lover of what he described as "legitimate crimes," such as hacking into his campaign website and social media accounts and posting phony messages that appeared to be from the sheriff.
According to Babeu, the Gila County authorities turned down the investigation, saying they simply didn't have the resources to tackle it.