Her statement also alleged physical abuse.
"He held me over a staircase and threatened to throw me down it. He picked me up over his shoulders and threw me onto concrete. He took pictures of my bruises and posted them online."
She said leaving the band was "the single most difficult decision I've ever made" but didn't regret it.
"It has taken me years to recover from enduring almost a decade of abuse, manipulation and psychological control. I am still recovering."
Kath told Pitchfork he was consulting lawyers and denied Glass' claims, calling them "pure fiction".
He said he was "outraged and hurt by the recent statements made by Alice about me and our prior relationship".
"Fortunately, there are many witnesses who can and will confirm that I was never abusive to Alice."
Since leaving in 2014, Glass was replaced by Edith Frances and the new-look Crystal Castles released one album in 2016 and performed in Auckland earlier this year.
Where to get help:
If it is an emergency and you or someone you know is at risk, call 111.
• Women's Refuge: 0800 733 843
• Victim Support: 0800 842 846
• Lifeline: (09) 522 2999
• Family Violence Info Line: 0800 456 450
