In addition to her song, a tune from the musical "Wicked" that at one point she forgot the lyrics to, Jones managed to make an eyebrow-raising comment about Arpaio, who was recently slapped with by a federal judge over his treatment of immigrants.
"It turns out that [Arpaio] does a lot of cool stuff that nobody knows about," Jones said at one point. "Do you know this guy goes down into the desert and puts out water so people won't die coming across the Rio Grande?"
The Rio Grande flows through Colorado, New Mexico and Texas. Officials for Arpaio's office said they had no knowledge of Arpaio ever putting water in the desert for people, according to Phoenix TV station KTVK, which broadcasted Jones' remarks.
In a separate interview, Jones was also asked about some of the hardline anti-illegal immigration policies that Arpaio prides himself on. In particular, KTVK asked Jones about the immigration sweeps by Arpaio's office, where deputies question people's citizenship status, even if they are stopped over a minor traffic violation.
"I honestly don't know about somebody pulling somebody over or targeting particular people," Jones said.
She also told KTVK she did not think Arpaio was a racist because most of his deputies were Hispanic.
"You might think he's a racist, but he's not. He actually has a majority of his officers that are of Hispanic decent," Jones told KTVK.
KTVK noted that only 24 percent of the staffers in Arpaio's office are Hispanic.
Besides Jones, Arizona Secretary of State Ken Bennett, state Sen. Al Melvin, and disbarred former Maricopa County Attorney Andrew Thomas are running in the Republican primary.
Watch the video of Jones singing below: