Mariah Carey's (search) troubled, HIV-positive sister has been arrested for prostitution — for a second time.

Suffolk County police said they picked up Alison Carey (search), 43, after she solicited an undercover cop at the West Shore Marina in Huntington, Long Island, on June 13.

"She offered to engage in sexual conduct for $250 in cash," a police source said.

Explaining the long lag time between Carey's arrest and the public release of her family ties, another source said, "We don't ask for the family tree when someone is put under arrest for prostitution."

It was Alison's second prostitution arrest.

She was previously busted in April at her Huntington home, police said. She pleaded guilty to disorderly conduct and was fined $200 on June 2.

Eleven days later, she was back on the streets, police said. The new charge carries a maximum of three months in jail.

Alison Carey has been out of tune with her family for years. She has claimed in interviews that she started turning tricks as a teenager, and that her work paid for limos that took her younger sister to her early gigs.

In the early 1990s, Alison was so broke and strung out that her mother got custody of the young woman's son.

She gave birth to another boy, and spent years in welfare motels and sleeping in a car. But she later lost custody of that boy, too.

In 2000, she shopped a tell-all book about her life and her famous sister, whom she called a "vain and heartless multimillionaire." The book was never published, if it was written at all.

A spokeswoman for Mariah Carey did not return a call yesterday.

Alison Carey's lawyer could not be reached.

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