WASHINGTON — Saying the opioid crisis requires bold measures, the state of Arizona filed an audacious lawsuit in the Supreme Court on Wednesday asking the justices to order members of the Sackler family, which owns Purdue Pharma, to return what the state said were billions of dollars looted from the company.

“We want the Supreme Court to make sure that we hold accountable those individuals who are responsible for this epidemic,” said Mark Brnovich, Arizona’s attorney general. “We allege that the Sacklers have siphoned billions of dollars from Purdue in recent years. They did this while knowing the company was facing massive financial liabilities.”

Lawsuits making similar claims have been brought in several state courts. What distinguishes the new suit is that it was filed directly in the Supreme Court, which almost never hears cases until after lower courts have considered them.

“I do think it’s a long shot,” Mr. Brnovich said. “It’s a little different. It’s a little unorthodox. Sometimes you’ve just got to throw deep.”