The documents say Heather – who has a seven-year-old daughter, Beatrice, with the former Beatles star - told one of the publicists: "I could kill [Paul] last night, he tried to choke me. The marriage is over."
However, sources at the company believe Heather was lying and fabricated the stories up in a bid to win sympathy.
The suit – which has been obtained by gossip website TMZ – also claims Heather was given the chance to appear on US TV show ‘Celebrity Apprentice’ but would only appear if Donald Trump would guarantee she would win, something he refused to do.
Heather, 43, is also accused of lying when she said all the money she earned from her appearance on ‘Dancing with the Stars’ in 2007 would go to charity, with the firm claiming only a portion did.
The publicity company is suing for unpaid fees totalling $168,000.
Heather got divorced from Paul in 2008 and she was awarded £24.3 million in the settlement.