It added: "Auckland DHB takes patient confidentiality extremely seriously and we are investigating this in line with our usual practice."
No further details were provided.
The Herald has also contacted a spokeswoman for Dalton's family for comment.
Patients' privacy has been breached on a number of occasions at New Zealand DHBs over the past few years.
Last year the Herald reported more than 70 upper North Island health workers had been disciplined for snooping into patients' records in the previous three years.
In 2013, four clinicians at Canterbury DHB faced disciplinary action after accessing cricketer Jesse Ryder's medical records.
Health workers who access confidential health records and information of a patient they are not directly involved with is a breach of the Health Information Privacy Code 1994.
The code sets out specific rules for the health sector to ensure the protection of individual privacy, and covers DHBs, as well as the Ministry of Health, ACC and health insurers.
Under the code, health agencies must take reasonable security safeguards to protect health information, including keeping confidential information safe from unauthorised access or disclosure.
There can be financial consequences for agencies that breach the rules.
Dalton collapsed on Thursday night. She was treated on the field at Northcote's Onewa Domain, bleeding profusely from the mouth and nose.
Her injuries did not come from any impact during the game, she was running when she collapsed.
Her husband, Duane Dalton, told the Herald on Sunday last week that it was "every husband and father's worst nightmare".
"All I can say is that Tarn is once again showing us what an incredible battler she is and, right now, she is putting up the fight of her life.
"We couldn't be prouder of her or love her more."
Dalton played for the Silver Ferns during 37 tests, playing goal shoot and goal attack from 1996-2007.
She is now a Sky TV commentator, and has been involved with the Takapuna Rugby Football Club, where her children play, and plays in a social touch rugby team on Thursdays.