Tabloid reports back in 2013 claimed the two pros were left raging at one another following a major row behind the scenes.
Now Ola has given her side of events in new autobiography, Strictly Ola: My Story.
"Towards the end of October we were told we were going to be doing a hip-hop number for a group dance on the Halloween show," Ola recalls in a passage released to the Daily Mail newspaper. "All the pros gathered in the studio at Elstree early on a Monday to learn the dance, after which we’d all go off and train with our celebs.
Ola says she and husband James Jordan found some of the steps difficult and asked if they could be changed.
The performer goes on: "Karen then shouted directly at me. ‘Why don’t you just get on with it?’ Kevin shouted at me too, and they both just started going crazy.
"I was taken aback and all of a sudden Karen was right in my face, shouting at me and waving her arms. It was completely over the top and I could feel my pulse racing."
Ola claims that things almost got physical as the row intensified: "She screamed something in my face. It was a vile threat, although she denies it.
"Karen was inches from me. Fellow professional dancers Pasha Kovalev and Artem Chigvintsev rushed forward and pulled Karen away.
"I tried to compose myself but it was no good. Two minutes later I ran out of the studio and burst into tears, and then Pasha and Artem ran out to find James."
Later the pair clashed again, with Karen allegedly branding Ola a "s*** dancer".
However Ola says it's now all behind them.
"It took a bit of time, but Karen and I did patch things up and we are fine now," she says.
Strictly Ola: My Story, by Ola Jordan will be released later this month. You can pre-order the book on Amazon here