A Melbourne couple infected with COVID-19 while on a skiing holiday in the United States have been the subject of repeated police complaints after they allegedly flouted advice to self-isolate and visited shops and a golf course on the Mornington Peninsula instead.

A wealthy finance industry figure and his partner were two of about a dozen Australians believed to have contracted the coronavirus after attending a social function in the exclusive alpine resort of Aspen, Colorado, earlier this month.

The sun shines down on Aspen, Colorado, earlier this month. A number of infections have been confirmed at the ski resort. Credit:The Aspen Times/AP

The Age and Sydney Morning Herald have been told by multiple sources that at least two other Australians who attended the event refused to be tested in Aspen because they were reluctant to interrupt their ski trips.

The couple, whom The Age and Sydney Morning Herald have decided not to name for legal reasons, returned to Melbourne on March 6 and four days later were informed by Victorian health authorities that they were at high risk of infection because of the outbreak in Aspen.