The former Green MP has filed for an injunction seeking to stop the party holding its meeting, planned for this Sunday.
Tana appeared at the High Court at Auckland on Thursday alongside her lawyer Sharyn Green.
Her judicial review is targeted at co-leaders Chlöe Swarbrick and Marama Davidson, the party's kaunihera (executive committee) and the party itself, over the decision to commission an independent investigation.
Tana's argument is the investigation was unlawful and not allowed by the party's own rules, and it was unreasonable of the party to commission the report or use its findings. She also claims unfairness and says she was "induced to resign her membership" of the party.
The Greens promised not to eject Tana by using the waka-jumping law until the court had ruled on the matters raised by Tana, and would cancel their September 1 meeting.
Tana's lawyer requested that these promises be set down as court orders, and the court did so - with no objection from the Green Party. The Greens requested an urgent hearing as soon as possible, and the judge - Justice Simon Moore - agreed the case should be given priority.
Green told him both parties had reached an agreement and would defer to a substantive hearing until September 12.
"You've been able, between the two of you, to sort out the road forward," Justice Simon Moore said.
"Thank you for your obvious co-operation."
Party says holding meeting could have meant longer court process
In a statement, Swarbrick said the party would defer the meeting until legal proceedings were concluded.
"The Greens have no desire to be caught up in protracted legal proceedings and are doing everything we can to ensure things progress without undue delay," she said.
"We will, unfortunately, not be able to confirm a new date until we are confident in the appropriate conclusion of legal proceedings."
Green Party musterer Ricardo Menéndez March told Midday Report the agreement was to postpone the meeting until after the September 12 hearing, and it was because going ahead could have meant spending longer in court.
"Trying to go ahead with the meeting could end up resulting in protracted legal proceedings and that's not in the interests of our members because they've worked really hard to get us to this point and we want to make sure that we can have this issue concluded.
"I think everyone, including our members and voters, want this issue to be over. And so that's why we're moving with those principles in mind."
Speaking to media at Parliament earlier, March said they did not feel outmanoeuvred by Tana and the meeting was being postponed to avoid further delays to the case.
"No, because what we're trying to do is avoid this becoming protracted. As you would have seen this is quite a novel way to approach things and I think Darleen will have to answer as to ... why these approaches are being tested out.
"We're not being pushed around, if anything we think that trying to go ahead would have resulted in protracted proceedings and we don't think that would have been fair to our members."
He said the party's view was if the meeting had not been delayed, the overall process would become more drawn out.
"I do want to make it clear that this is about making sure that this does not [get] drawn out longer than it already has," he said.
"We've been really clear that our values and principles are also moving forward with a tikanga-led approach, and that requires the other party showing accountability which has not happened so far.
"We've made it clear abundantly many many times that part of the reason we're undertaking this process is we don't believe that the [waka-jumping] law should be used in a way which concentrates power in the leadership."
Asked if it was possible the meeting could be postponed indefinitely, March refused to speculate.
"That's a hypothetical that I'm in no position to indulge in at this moment."
Swarbrick said the party would continue to be transparent about the proceedings.