BAILLIEU government MP Geoff Shaw is under police investigation over allegations of misconduct in public office.

The Victoria Police investigation follows an opposition complaint made about Mr Shaw. The complaint came in the wake of a damning Ombudsman's report in October into the Frankston MP's conduct.

Baillieu government MP Geoff Shaw. Credit:Pat Scala

Victorian Ombudsman George Brouwer found Mr Shaw had used his taxpayer-funded Ford Territory and fuel card to run his hardware business, and had provided misleading information about it under oath.

A police spokeswoman on Friday confirmed there was now an investigation under way. She said: ''Victoria Police can confirm that the crime command is investigating allegations of misconduct in public office by a serving member of the Victorian Parliament and the investigation is ongoing.''

The investigation comes as a result of a complaint from opposition scrutiny of government spokesman Martin Pakula. He made the complaint about Mr Shaw in October to police Chief Commissioner Ken Lay. He said the opposition had maintained from day one that investigating Mr Shaw's conduct was a police matter rather than the government's own parliamentary committee.

''It seems the police agree. Ted Baillieu should have sent Geoff Shaw packing from the Parliamentary Liberal Party weeks ago, and he should do so now without further delay,'' Mr Pakula said.

No charges have been laid.