Prime Minister Julia Gillard won some form of political reprieve Thursday as the New South Wales state police declared it will cease further investigation of Labor MP accused of using union funds to hire prostitutes.

"There is no basis for a formal investigation into any offence under New South Wales law," NSW police officials said in a statement, which relieved Craig Thomson of further worries from threats of investigation.

The development, political observers said, also came as a relief for Gillard following policy setbacks suffered by her government, which were compounded by her sinking poll numbers as earlier published by The Australian this week.

According to the Agence France-Presse, Thomson was accused of using a credit card issued to him by the Health Services Union in 2003 and 2005 in paying for prostitutes.

Thomson, who served as the union's national secretary at that time, dismissed the allegations and filed defamation lawsuits against two newspapers that published the reports two years ago.

Reuters has reported that acquiring the services of prostitutes is legal in Australia but Thomson was subjected to investigation on accusations that he illegally utilised the funds entrusted to him by the union he served.

Now freed from the scandal, Thomson also escaped the possibility of being expelled from the Parliament, which is a gain for Gillard as every seat counts for the embattled prime minister in light of recent speculations that internal and external threats could force her out soon.

Talks of Kevin Rudd's return to Labor Party leadership are swirling around while national surveys indicated that Opposition Leader Tony Abbott could drive out Gillard out of office if elections were to be held today.

Federal Treasurer Wayne Swan, who also serves as Gillard's deputy, said that the closure of Thomson's legal woes should put a stop to political mud-slinging and unfounded speculation.

"If people have got allegations to make they should be dealt with in the normal way, free from the lynch-mob mentality which the Liberal Party is pursuing," Swan declared during an interview with ABC Radio on the same day.

At present, Labor holds a one-seat edge against the Coalition headed by Abbott's Liberal Party, but Gillard's partnership with independent MPs and the Australian Green Party assures it of power until at least the next national elections scheduled on 2013.

Ms Gillard enjoys both the support of her Greens and independent allies, according to Reuters, yet silent but bigger threats could come from within her own party, analysts said.