(CNN) -- An Arizona state senator involved in an apparent freeway-shoulder scuffle with his girlfriend was not detained because he has immunity from arrest while the legislature is in session, police said.

Officers in Phoenix who were called to investigate a reported altercation found that both Sen. Scott Bundgaard and his girlfriend, Aubry Ballard, had marks suggesting a physical dispute, police spokesman Sgt. Tommy Thompson said.

Bundgaard, a Republican and the state senate's majority leader, was allowed to go -- although prosecutors will review the case and could later file charges, Thompson said. Ballard was arrested on suspicion of misdemeanor assault and taken to jail.

In a joint statement Sunday, Bundgaard and Ballard said they were "tired and embarrassed" because of the incident.

"We want to jointly apologize for allowing a private matter to interrupt the public -- and especially for taking up the valuable time of law enforcement. The police officers who responded deserve thanks for their sensitivity and compassion," they said.

Bundgaard said the dispute began on the way home from a charity "Dancing with the Stars" fundraiser, after Ballard accused him of "inappropriately touching" his dance partner.

"She proceeded to throw my clothes and other things out of my car on a freeway as I took her home," Bundgaard said in a statement Saturday.

The senator said he tried to stop his girlfriend from punching him, which resulted in marks on her knees.

Bundgaard said he pulled Ballard out of the car, but denied ever hitting or pushing her.

"I have never inappropriately touched a woman and never would. There was no domestic violence," Bundgaard said.

Ballard described the incident as "the absolute worst night of my life" in her own statement released Saturday.

"To go from putting on a beautiful dress for a great date to a fundraiser to ending up on the side of a freeway? I don't have another tear left to cry," she said. "I'm still trying to get my mind around a few things: Scott's actions, the 17 hours I spent in jail awaiting processing, my bruises, scrapes and soreness and his statements to the media."

Their statement Sunday said the couple were breaking up and appealed for privacy.

Arizona's constitution says legislators are immune from arrest "in all cases except treason, felony, and breach of the peace" and allows them immunity from civil process while the legislator is in session.

Phoenix police said they will submit the case to the city attorney's office for review, Thompson said.

In his statement, Bundgaard said he will not hide behind his privilege.

"I waive any and all 'immunity.' If I did something wrong, charge me," he said.