Officers are investigating a complaint made by a shareholder that Wallace made misleading statements about finances at December's AGM at Ibrox, therefore constituting a breach of the Companies Act.
King claims Wallace spoke with the board's consent and also claims that it did not challenge his assertion that there were sufficient funds available.
At the club's AGM Wallace insisted there was enough money to keep the club trading in the short term but in February, a $2.73 million loan was sought from two shareholders to meet running costs.
A supporters coalition group, the
Rangers responded by insisting the complaint has 'no grounds' but King was adamant on Monday night that Wallace and his fellow directors were aware that there was a cash shortfall.
A statement from King released to a number of news organisations read: "The CEO is now subject to a criminal complaint, but I believe his comments were made with the full knowledge of the board.
"It is seriously wrong for this board to state in the review that at the time of the AGM the board, and the CEO in particular, believed that there was sufficient cash to last until the end of the current season.
"It is beyond doubt that the CEO and other board members [were] aware last December that there was insufficient cash. The CEO is now subject to a criminal complaint, but I believe that his comments were made with the full knowledge of the board.
"Certainly no one came out to contradict him. We should therefore expect any criminal investigation to extend to other board members. It is telling that
"If cash was wasted as a result of mismanagement - presumably
A statement released by Rangers from chairman
"He will continue to develop the club's long-term future plan which will return us to the top of Scottish football and competing in
"Any suggestions of inappropriate behaviour by him in relation to his duties as Chief Executive Officer are odious and unfounded.
"They will be defended with full rigour, if a substantiated complaint is ever put to him or Rangers.
"The history and facts have been explained in both the Interim Statement and the Business Review summary.
"Any media reports to the contrary are based on rumour and gossip which is damaging to the football club.
"If Mr King wishes to engage in constructive dialogue, then the door remains open.
"Regrettably however, he continues to make fictitious, inaccurate and misleading comments which are very unhelpful."
King was scathing of other aspects of Wallace's document which, among a wish list, included aims for Rangers to be Scottish Premiership champion by 2016-2017, calling it 'a great review for Celtic fans'.
He said: "This flimsy review is completely superficial and could have been put together in a day by a relatively junior employee.
"It falls well short of the strategic business review that we were promised.
"There is nothing to read between the lines, no sign of a coherent plan to save this club, and more importantly no hope for the supporters or shareholders.
"I would reject it if one of my CEOs presented such a summary review to me.
"In truth, it is this board's stubborn refusal to secure fresh equity that is the cause of the present fragile state of the club's finances.
"The board clearly hoped to muddle along by using the season ticket advances from fans.
"This review should reinforce to fans that this board cannot serve as an appropriate custodian for their season ticket money.
"Fans could once again lose their season ticket advances if given to the club at this time. It is unconscionable that this board has done nothing to bolster the finances since the last AGM."