Federal Labor MP Craig Thomson will not be subject to a criminal investigation by New South Wales Police.

Mr Thomson, whose seat plays a critical role in the Gillard government's balance of power, is under pressure over how his Health Services Union credit card was used to pay for prostitutes while he was heading up the union.

The Member for Dobell has admitted authorising the payment to an escort service in 2005 - but has said another man used the card and forged his signature.

In a statement issued overnight, police said there was no basis for a formal investigation into any offence under New South Wales law.

Police media spokeswoman Joanne Elliot says the State Crime Fraud and Cyber Crime Squad made its assessment after receiving a letter from shadow attorney-general George Brandis about the credit card's use.

"Based on the subsequent material and information provided to NSW Police by the Health Services Union, including a 120-page document relating to their own examination of the use of Mr Thomson's credit card, it was concluded that based on the accounting practices of the union relating to the use of corporate credit cards there was no evidence to warrant a formal investigation by NSW police," she said.

However, NSW Police are sending the material to Victorian Police because the financial controls of the Health Services Union are conducted out of the Melbourne office.

Police in Victoria have told the ABC they are waiting for the referral from NSW, and will assess it before deciding what action should be taken.

Senator Brandis has told AM he does not owe Mr Thomson an apology.

"Not at all," he said.

"The police in New South Wales have decided that, regardless of what you think of that, they don't consider it reaches the threshold of a prosecution. But the facts remain."

But Deputy Prime Minister Wayne Swan told Radio National Breakfast that the comments by NSW Police are clear.

"I notice that Mr Brandis is still out there throwing mud again this morning, but this is quite a categorical statement."