"Every time I've tried to talk with her, it's dangerous," Richards said while sitting down with Andy Cohen during an upcoming Watch What Happens Live! special. "She confronts me in a not-so-nice way."
The topic was raised by a caller who asked what Richards what she would say to Rinna if they were face-to-face.
"I did try to speak with her and ask her why she kind of has it out for me. I don't get it," Richards shared. "It's been almost two years since I've seen her, and [she says] I'm a viscious, vile dog, and I'm crazy. It's concerning to me why somebody, after two years, [is] scared of me? I don't get that."
The 51-year-old reality star also opened up about getting arrested for public intoxication at the Beverly Hills Hotel in April 2015.
"I drank that night, you know? No excuses," said Richards, who explained that she had been "working the program" and was coming up on three and a half years of sobriety, but had fallen off the wagon due to personal problems in her life.
"I stopped focusing on myself. I stopped taking the time for me and going to meetings because I was taking care of other people and stopped caring for myself."
According to Richards, she had a few drinks while visiting her daughter, Brooke Brinson, but felt "horribly guilty" about imbibing at her daughter's house, so she left. Soon after, she pulled in to the Beverly Hills Hotel to avoid drinking and driving.
After walking into the hotel's bar, Richards said she asked to sit in the booth she used to frequent back when she was a regular at the hotel.
"I said, 'Please, I'm staying. I don't want to drive. I'm scared.' And [an employee said], 'No, if you don't leave, we are calling the police.' And I really thought he was joking. And he called the police, and one thing lead to another."
Richards' full WWHL one-on-one interview airs Tuesday at 8:30 p.m. ET/PT on Bravo.