A source told the Weekend Herald eyebrows were raised when Murray finally disclosed his expenses to staff because some of the spending allegedly could not be accounted for.
Simcock told the Herald in February he was comfortable with Murray's comparatively high expenses because of his role as lead chief executive on national health groups.
He added they were skewed because of the moving costs and said the board would be making sure the expenses did not "grow too much".
Murray declined to answer questions at the time.
It's understood Murray has since reimbursed some of the spending but it's not clear how much.
His latest expenses for the 2016/17 year, along with those of other DHB chief executives, are due now.
Waikato-based Labour MP Sue Moroney said she had been told the spending in question was on the chief executive's credit card.
"My understanding is that the investigation covers two financial years of unauthorised and unexplained spending."
She queried why the board had not acted earlier given the alleged staff concerns, the delay in disclosure, the size of Murray's expenses and the fact they were made public in January.
A Waikato DHB spokeswoman said the DHB had no comment.
Questions put to Murray through the spokeswoman went unanswered.
A spokeswoman for the Minister of Health, Dr Jonathan Coleman, said the issue had been flagged with Coleman's office but referred questions to the DHB.