In a statement on Tuesday, the Department of Home Affairs confirmed it has “stakeholder arrangements” with several large international organizations for speedy processing of short stay visas, but insisted there was no special treatment given to applicants.

The department said the arrangement with Crown ended in 2016.

In 2017, a court in Shanghai sentenced three Australian employees of Crown to prison for illegally promoting gambling in China.

Separately, court transcripts in China show Mr. Zhou, who is also known as Zhou Jiuming, has been named in several civil and criminal cases including one that accuses him of misappropriating “a huge amount” of funds. That same case references separate criminal charges against him and cites investigations by the police for economic crimes in Wuhan, China. Details of Mr. Zhou’s criminal charges are not publicly available.

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Mr. Zhou and Mr. Chai were business partners through companies registered in Hong Kong and Australia that are suspected of being set up simply to move large sums of money out of China to Australia, according to a person familiar with the companies, and the Australian authorities .

Mr. Chai is listed in several internal Crown documents as one of the company’s V.V.I.P.s, or Very Very Important Persons. One internal record shows he had spent $28 million (41 million Australian dollars) over 18 months starting in June of 2012, and in the following year he was listed as one of Crown’s top 50 customers based on gambling turnover.

It is not clear when he became an Australian citizen, but corporate registrations with his Australian passport go as far back as 2005.

Among the questions being asked now, Australian officials said, is whether Mr. Chai is simply a partner of Mr. Zhou, or has played a broader role with other Communist Party officials who the authorities believe might have been trying to launder money through Australian casinos, or move money to finance foreign interference or espionage in Australia.

Several of the Chinese-Australian groups Mr. Zhou has been involved with in Australia, including the Hubei Association of Australia and Huaxing Arts Group of Melbourne have been described by analysts as closely aligned with the United Front Work Department, a muscular agency that presses for support of the Communist Party agenda abroad. United Front associates have been linked with campaign contributions and other efforts to influence Australian politics.