Days after Senator Lidia Thorpe referred the Northern Territory's Attorney-General to the Territory's corruption watchdog, the Attorney-General's Department has taken the unusual step of publicly releasing emails between the NT's top judge and senior government bureaucrats.

The release follows the publication of a leaked email from Chief Justice Michael Grant AO to Acting Chief Executive of the Department, Leonique Swart, accusing the Department of blocking the release of a media statement to The Australian newspaper.

On Tuesday, Senator Thorpe referred Attorney-General Marie-Clare Boothby to the NT Independent Commissioner Against Corruption (ICAC), calling for a full investigation.

A Department spokesperson told the ABC on Thursday that the emails - seen by National Indigenous Times and showing a conversation between Chief Justice Grant and Ms Swart on October 8 - demonstrate that the Department "never intended to intervene" in the court's media processes and that the matter "did not involve the Attorney-General".

In the emails, Chief Justice Grant wrote to Ms Swart, saying he had been advised she "recently and unilaterally directed the Court's media liaison officer not to send a communication to The Australian newspaper which I requested him to send".

He said he was "extremely disturbed that you have purported to interfere with the Court's independence and operations in this fashion, and more disturbed that you have done so without making any attempt to discuss the matter with me".

"Please confirm without delay that you will no longer seek to interfere in this well-established function of the Supreme Court, and that you will not purport to exercise any right of veto concerning statements by the Supreme Court to media organisations under the name of a 'Court spokesperson'," he added.

View this post on Instagram

A post shared by National Indigenous Times (@natindigtimes)

Ms Swart denied any interference, saying there had been a "number of misunderstandings." She said she "did not intend to veto the court" by declining to approve a correction in a court media statement.

"I was under the apprehension I was being asked to approve a correction being released by the Attorney-General's Department which at the time I did not approve. That apprehension was, now that matters have been made clearer to me, in error," she said.

She added: "Finally, I can assure you I have full respect for the separation of powers and I defend it frequently."

Both the Court's media office and the Department have described the issue as a "misunderstanding" that had been resolved. The emails reviewed by National Indigenous Times show no evidence of improper influence from the Department.

The exchange followed The Australian's coverage of the sentencing of Indigenous man Stephen Rioli, which it linked to the case of Jake Danby - whose hit-and-run sentence sparked national outrage. The emails asked for corrections to the article for linking the two cases.

On September 22, National Indigenous Times published details of Mr Rioli's sentencing, directly citing The Australian's reporting.

In her ICAC referral, Senator Thorpe raised concerns over Attorney-General Boothby's undisclosed family connection to Mr Danby - her sister's stepson. It was a connection Ms Boothby had not previously disclosed publicly, despite speaking to reporters about the case and sentencing.

Only after the familial relationship was revealed by the NT Independent, did Ms Boothby say she informed CLP leader Lia Finocchiaro "immediately" after the accident last year, and denied any wrongdoing.

Ms Finocchiaro has since defended Ms Boothby, saying she has "full confidence" in her.

National Indigenous Times does not suggest Ms Boothby has done anything untoward or outside the realms of her role, only that there has been a submission to ICAC. Ms Boothby declined to comment when contacted by National Indigenous Times on Wednesday about the ICAC referral.

Senator Thorpe said she had referred Ms Boothby to ICAC because there are "serious questions about what's been going on with the Danby hit-and-run case," including the delay in Ms Boothby admitting her connection to Mr Danby.

"ICAC needs to get to the bottom of this, and the NT Attorney-General can't just shrug it off. If she [Ms Boothby] denies involvement, she should welcome an ICAC investigation," she said on Wednesday