Cook previously produced podcast Cooking the Books for NZME. She said when she started it, it was made clear that it was not part of her job but she was allowed to run it in her spare time, with it being distributed by NZME.
But she now alleges she was forced into a position where she had to give it up to her former employer.
NZME disputes her claims.
"The company went through a few mergers along the way and the original mission was lost," she told followers on her Facebook page. "They decided they did own it. I told them they didn't but because I still worked for them and had no need to make money from it, no need to fight right?"
But she said before she went on her second period of maternity leave she had a new boss, who told her she would be replaced while she was away.
"Despite having written permission to start my business providing financial education they now want to 'revisit' that. I'll be required to show them behind the scenes, the financials, how I'm running it and they may require me to close it down. Like hell."
She said the process led to her resigning and having Cooking the Books "taken" from her.
NZME has now rebranded the podcast the Prosperity Project, presented by Nadine Higgins.
Cook said anyone who listened to her rebranded podcast could "feel free to unsubscribe". "If you happen to leave a one-star review on your way out the door, I certainly couldn't stop you."
Employment lawyer Alison Maelzer, of Hesketh Henry, said it was hard to comment without all the facts. Things like the details of Cook's employment agreement and any other agreements about side projects or policies would be important in determining "who owns what".
But she said in general an employer had a right to intellectual property that an employee created in their work.
"What I can say is that in general, an employer will have rights to intellectual property that an employee creates as part of their work.
"So for example, if I create a particularly stylish work-from-home policy as part of my job, my employer will own the rights to that, and could stop me (a) taking it away if I left employment, and (b) using it for my own benefit, or the benefit of someone else (eg a new employer).
"Most employment agreements will seek to expand the employer's rights to the intellectual property, by providing that any work that relates to the employment, created while the person is in employment, whether on work time or not, will belong to the employer. If there was some other agreement between the parties then the terms of that agreement would obviously be very relevant as to who owned the intellectual property in the side project."
NZ Herald editor-in-chief Murray Kirkness said it rejected Cook's claims about NZME and the podcast. "We have advised her of our position."
