Mr Biden claimed the two men had been sent a copy of his hard drive by the owner of a computer shop where he is thought to have left his laptop for repairs.
He said they had spent an “extraordinary amount of time and energy toward looking for, hacking into, tampering with, manipulating, copying, disseminating and generally obsessing over data” from the laptop.
Mr Giuliani is alleged to have taken data from the laptop, which suggested Joe Biden had met with his son’s Ukrainian employers, and given it to reporters from The New York Post.
The allegation that the president had inappropriate involvement in his son’s business dealings has since become the centre of a Republican impeachment inquiry in Congress.
Mr Giuliani has repeatedly discussed Mr Biden’s laptop and claimed he had access to its contents.
In February of this year, during an episode of his show, America’s Mayor Live, Mr Giuliani held up a laptop and told viewers: “This belongs to Hunter Biden.”
The lawsuit claims the former New York mayor then “proceeded to brag about having copied [Hunter Biden’s] data onto his own computer and about having accessed, analysed and manipulated the transferred data”.
It also claims that Mr Giuliani and Mr Costello, his former lawyer, breached both state and federal data privacy laws in relation to a hard drive allegedly copied from his laptop.
‘Political nuclear weapon’
Mr Biden claims that Mr Giuliani was first given access to his data when he was contacted by John Paul Mac Isaac, the former owner of a Delaware computer repair shop where he had reportedly left the machine.
The lawsuit claims Mr Mac Isaac contacted Mr Costello and Mr Giuliani using a contact form on their website and told them he had been “trying quietly to bring it to people’s attention” for “almost a year”.
It says Mr Mac Isaac then sent a hard drive containing a copy of Mr Biden’s files to Mr Costello via FedEx, and claims the pair then accessed and “manipulated” the data.
Mr Biden’s lawyers referenced a story about the laptop published in New York Magazine in September 2022 which claimed Mr Costello had shown the data to a reporter and logged into a copy of Mr Biden’s hard drive using his name.
They also claimed the pair had worked with Steve Bannon on the hard drive, in what they are claimed to have referred to as “Project Manhattan” because it was a “political nuclear weapon”.
“Although defendants and their allies are entitled to their baseless opinions about the plaintiff and the Biden family … they are not entitled to violate federal and state anti-computer hacking laws to advance their personal and political agendas,” the lawsuit said.
Both Mr Biden and Mr Giuliani are already facing criminal charges in separate cases.
Mr Biden has been indicted for violating federal laws covering gun possession, after he allegedly purchased a handgun while addicted to illegal drugs.
The case has been brought by David Weiss, a government lawyer who has been given special counsel status to investigate the claims independently of the Department of Justice.
Mr Biden has already sued the Internal Revenue Service, alleging that a whistleblower from the agency had breached his privacy.
Data from his laptop has also been used to construct a case for impeachment by Republicans in the House, who are conducting an inquiry into his father.
They claim the president lent his legitimacy to his son’s business dealings while serving as Barack Obama’s vice president.
Meanwhile, Mr Giuliani has been indicted in Georgia in connection with Mr Trump’s attempts to overturn the 2020 election result in the state.
He is one of 18 co-defendants charged with an alleged “criminal enterprise” to prevent Mr Biden winning the presidential race.
Both have denied the respective criminal charges against them.
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