(CNN) John Clune, the attorney for the woman accusing Supreme Court nominee Brett Kavanaugh of exposing himself to her when they were in college, said only Democrats showed up for a phone call they had scheduled with Senate Judiciary Committee staff earlier Tuesday

Clune also said in an interview Tuesday on CNN's "Anderson Cooper 360" that Republicans seem to be "game-playing" and changing the rules for their communications.

Clune represents Deborah Ramirez, 53, who attended Yale with Kavanaugh and told Ronan Farrow and Jane Mayer of The New Yorker that she remembers Kavanaugh exposing himself to her at a dormitory party. Kavanaugh denies the allegation.

Clune told Anderson Cooper that his team has had a number of email communications with the committee, "but the difficulty is every time we try to set up a phone call, the majority party either changes the rules of the phone call or they want additional information as a condition of even having a phone call with us."

"We finally had a phone call scheduled for 7 o'clock Eastern this evening, we got on the phone, and only the minority party showed," Clune said. "So, feels like there's a lot of game-playing that's going on right now by the majority party."

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