The charge, laid by the Financial Markets Authority, carries a maximum penalty of five years in prison or fines of up to $300,000.
In the Crown's opening address today, prosecutor Steve Symon said the accused didn't take the appropriate steps to ensure the document was true.
"The Crown say Ms Braithwaite didn't delegate the decisions about things to other people. On the contrary she didn't do anything at all, she just didn't do her job as a director in terms of making sure she was sure about the information," Symon said.
Symon said it wasn't enough for Braithwaite to rely on Ludlow's word that the prospectus was true.
Ludlow was also a director of National Finance but is now in prison.
Symon said there were plenty of other people she could have asked to check the truth of the offer documents, including the company accountant and the trustee."
"Moreover if she had looked at the documents available to her she would have found out these statements were untrue," he said.
"The alarm bells should have been ringing very loudly for Ms Braithwaite."
Symon has been giving the jury a detailed run-down on what a prospectus is and other aspects of a finance company.
He will continue to deliver his opening address this afternoon.
Earlier this morning, Justice Pamela Andrews told the jury of 12 that there is no room for prejudice in the case.
"This trial is essentially about a finance company. You may have heard or read about trials of those who are directors of finance company, you may know someone who has invested in a finance company and you may have your own views about finance companies. During this trial, You put all of those views to one side, you deal with this trial solely on the basis on the evidence that is given in court and you keep open minds until you have heard all the evidence," Justice Andrews said.
Braithwaite had been due to appear in the dock with fellow director Anthony Banbrook, but the latter made an 11th-hour guilty plea. He will now be sentenced next month.
National Finance went into receivership in 2006, owing investors $21 million. Some investors have recovered 49c in the dollar.
Ludlow is serving a sentence of six years and four months after being convicted of charges laid by the Serious Fraud Office and the Financial Markets Authority.
He was found guilty last July of defrauding investors of an estimated $3.5 million.
He and Braithwaite once shared a $1.5 million Devonport property and in 2009 he blamed the stress of the business' failure for the pair's break-up.
Both are banned from being company directors until next April.
National Finance accountant John Gray pleaded guilty to theft and false accounting charges in the Auckland District Court in 2010 and was sentenced to nine months' home detention.