Following their introduction, Davis, 66, claimed Murray "insisted" on using a massage device on her.
"I said no multiple times, but he wouldn't relent," she wrote. "I would have had to yell at him and cause a scene if I was to get him to give up trying to force me to do it; the other men in the room did nothing to make it stop. I realized with profound sadness that I didn't yet have the ability to withstand this onslaught -- or to simply walk out."
The actress added that Murray ultimately "placed the thing on my back for a total of about two seconds."
Davis also discussed the alleged meeting in an interview with The Times UK.
"That was bad," she told the outlet. "The way he behaved at the first meeting ... I should have walked out of that or profoundly defended myself, in which case I wouldn't have got the part. I could have avoided that treatment if I’d known how to react or what to do during the audition. But, you know, I was so non-confrontational that I just didn't..."
After the journalist said she was "blaming herself for his behavior," Davis replied, "Ha. Point taken. There's no point in regretting things, and yet, here I was regretting. And yes, exactly, it wasn’t my fault."
Meanwhile, in her memoir, per People and The Times UK, the "Thelma & Louise" star also recalled an on-set moment between her and Murray, in which she alleged the actor yelled at her in front of the cast and crew for being late despite the fact that she was waiting on wardrobe, and continued to scream at her as she rushed to get to set.
"There were easily more than 300 people there -- and Murray was still screaming at me, for all to see and hear," Davis wrote.
Reflecting on her experience working with Murray, Davis told People, "I've never spoken about it publicly."
"For publicity, I saw him after we made the movie, but other than that, I haven't seen him or spoken to him," she later added. "I figure it's sort of rather universally known that he could be difficult to work with. And so I don't feel like I'm busting him in a way that will necessarily shock him. I think he knows very well the way he can behave."
TooFab has reached out to Murray's reps for comment.