SYDNEY, Australia — It was an extraordinary question for a member of Australia’s Parliament to be asked on live television: Are you a spokeswoman for the Chinese Communist Party?

“The simple answer,” the lawmaker, Gladys Liu, responded, “is no.”

But little else was simple about the interview that Ms. Liu — Australia’s first Chinese-born member of Parliament — gave last week to respond to reports of her not-long-ago membership in groups linked to the Communist Party.

Her fumbled answers, and the outcry that followed, have exposed the country’s struggle to integrate a growing community of immigrants from China who have tended to be overlooked by the political system except as a source of cash.

Two forces are now colliding: Australia’s ethnic Chinese community is increasing in size and power just as the country is becoming more skeptical of its economic dependence on China and raising alarms about Chinese influence in Australian institutions.