Whaitiri was stood down as a minister over what was described as a "staffing matter" while an employment investigation took place.
It has since been reported that a staff member who had recently joined Whaitiri's office as press secretary had been pushed during a heated argument.
Whaitiri was known to have had a number of staff pass through her office since being appointed Customs Minister.
McCready has taken successful court action against politicians in the past.
He brought the prosecution against former Act MP and government minister John Banks over his electoral donations, which led to a conviction being overturned on appeal.
He was also behind the 2007 case in which Labour's Trevor Mallard was convicted of assaulting National's Tau Henare.
His complaint to police also copies in the Prime Minister, who is referred to in the documents as " Lucinda Ardern".
McCready is a former bankrupt who has a number of convictions himself - one for trading while bankrupt, for making false tax returns and for blackmail.
Whaitiri's Customs portfolio has been passed to Kris Faafoi during the employment investigation.
She has also lost her agriculture, local government and Crown/Māori relations associate portfolios.
Whaitiri was the second minister to lose her roles in a week. Clare Curran was earlier demoted from Cabinet.
A police spokesperson confirmed a complaint had been received and was being considered.
