Richards, 50, was due to appear at a hearing Monday regarding the arrest but skipped out because of a foot injury.
"She didn't attend because she had some sort of injury to her foot, and therefore couldn't appear," Ricardo Santiago, spokesperson for the Los Angeles County District Attorney's office, tells PEOPLE. "The judge accepted the explanation and allowed her attorney to appear on her behalf."
Despite contradictory reports, Richards did not accept a plea deal: "There were conversations about a negotiated settlement being offered by our office, but the offer was rejected by the defense," Santiago says.
The deal that was offered included 36 months probation, 30 days community labor and 52 Alcoholics Anonymous classes. Richards' attorney rejected the deal because "they wanted community service instead of community labor," Santiago says, adding that a pre-trial court date is set for Sept. 14.
If the case goes to trial and Richards is found guilty, the reality star could face jail time.
The arrest took place April 16, after officers responded to a "report of a possible fight" at the Beverly Hills Hotel around 1:30 a.m. According to the police statement, Richards was taken into custody after "displaying symptoms of intoxication including slurred speech and belligerent insolent behavior cursing at the officers."
Though Richards, who has admitted she struggles with alcoholism, checked herself into rehab shortly afterward, she was charged with three misdemeanors: public intoxication, resisting arrest and battery on a cop. She was also barred from returning to the swanky hotel.
Richards left rehab in May to attend her daughter Brooke's wedding in Mexico and then returned to the facility two weeks later. She then left for a second time in June, and the mom of four grown children, who also cares for her ailing ex-husband Monty Brinson, was on her own again.
The troubled reality star was arrested again Aug. 2 for allegedly shoplifting close to $600 from a Target in Los Angeles. She spent the night in jail before posting a $5,000 bail.
A source told PEOPLE at the time of Richards' second arrest that "no one understands what she's doing" and that the former child actress is still not speaking to her sister Kyle, 46.
"Her family is so concerned. And they're fed up. She's cut herself off from friends and family who care about her," continued the source, adding that Richards lacked a stable living situation and "mismanaged her money."
Because of her ongoing struggles with sobriety, Richards will not be returning for the next season of Real Housewives of Beverly Hills, a decision her costar Lisa Vanderpump supports.
"I'm sorry that Kim's not here because of the situation … but I think that her sobriety is more important than any reality show," Vanderpump told PEOPLE on Aug. 13.