It's believed concerns about Murray's expenses were first raised by staff last year.
In December Murray came under fire by Government watchdog the State Services Commission after the Herald revealed he had not filed expenses for his first two financial years in the role.
When they were finally disclosed in January this year the expenses showed Murray had spent $108,000 of taxpayers' money on international and domestic travel for the job.
By comparison his predecessor at Waikato DHB, former chief executive Craig Climo, spent $17,670 in a two-year period.
When the Herald asked chairman Bob Simcock about Murray's comparatively high expenses in February, Simcock said he was comfortable with them and that they included $36,000 worth of relocation costs from Murray's former job in Canada to Hamilton, which skewed the total.
The relocation costs included $11,710 for early arrival accommodation costs because Murray finished his role at Fraser Health in British Columbia earlier than expected.
It's understood these costs were a focus of the investigation, and accounted for three months' accommodation.
When the investigation was first launched Simcock told the Herald its outcome would first be reported to the board's remuneration committee, and then to the board with the public excluded.
Simcock has not responded to repeated questions from the Herald around the progress of the investigation and whether the remuneration committee has met.
Acting chief executive Neville Hablous said in late September that the remuneration committee, which includes Simcock, deputy chair Sally Webb, and board members Sally Christie, Tania Hodges and Crystal Beavis, last met on August 4 and only meets at the behest of the chair.
"The committee is concerned primarily with the payment and performance of the chief executive."
The Herald understands the committee was to meet last week, but questions on the issue today went unanswered.
A DHB spokeswoman previously refused to answer further questions on the subject and said the DHB could not comment while the investigation is ongoing.
Multiple requests made by the Herald under the Official Information Act for information relating to Murray's expenses have been declined by the DHB.