Maricopa County Sheriff Joe Arpaio’s own lawyers will have a chance to question the sheriff when he takes the stand again today in the contempt of court hearings against him. Arpaio and four others are facing contempt of court for violating a judge's orders in a racial profiling lawsuit.

Meanwhile, Maricopa County is asking the U.S. Supreme Court to intervene in a technical dispute in the case.

Back in April, the 9th U.S. Circuit Court of Appeals upheld most of the judge’s racial profiling ruling against the sheriff’s office. The appeals court also decided Maricopa County should be the named defendant in the lawsuit, not the Maricopa County Sheriff’s Office..

That hasn’t sat well with county officials like county Attorney Bill Montgomery.

“This particular ruling runs afoul of basic rules of civil procedure, basic rules of fairness,” Montgomery said of the 9th Circuit decision.

Montgomery said the ruling doesn’t make sense under Arizona law because the county board of supervisors doesn’t have full authority over the sheriff, who is a constitutional officer.

So the county is asking the US Supreme Court to intervene to take the county’s name off the lawsuit.

“At the end of the day it is a technical correction,” said County Supervisor Steve Gallardo.

Gallardo voted to move forward with the appeal, but he said at the same time, he has reservations about racking up even more legal bills.

“The taxpayers are still paying the bill, and we are way in the hundreds of millions of dollars now on lawsuits now,” Gallardo said. “So at what point do we say, enough is enough? How do we stop the bleeding?”

Thursday marks the 11th day of the contempt hearing and there are more days ahead.

Since the county became a named defendant in the case, the county has been incurring even more costs during these hearings. That’s because Montgomery appointed private lawyers to represent county’s interests in the case.

Judge Snow, however, has said he is skeptical that the county needs separate representation from the sheriff and sheriff’s office employees in the case.