WASHINGTON — A unanimous Supreme Court on Tuesday upheld a jury verdict that State Farm Fire and Casualty Co. committed fraud against the federal government after 2005’s Hurricane Katrina.

The justices on Tuesday rejected claims by State Farm that the whistleblower case against the insurer should have been dismissed because its existence was leaked while it was supposed to be secret.

Justice Anthony Kennedy wrote for the court in upholding an appellate ruling that there is no requirement in federal law that the lawsuit be dismissed.

Sisters Cori and Kerry Rigsby filed the fraud lawsuit on behalf of the government after they said they witnessed State Farm shifting Mississippi claims to federal flood insurance that should have been paid by private wind insurance.

The Rigsbys won their case in 2013, focused on one home in North Biloxi, Mississippi. State Farm was ordered to pay $750,000 in damages, with 30 percent going to the Rigsbys and the rest going to the federal government. Their lawyers won $2.9 million in legal fees and expenses. The Rigsby sisters worked as independent adjusters for State Farm following Katrina.

More importantly, their case gave rise to other claims that Illinois-based State Farm defrauded the National Flood Insurance Program. Last year, Mississippi filed its own civil fraud lawsuit against State Farm, saying the state paid as much as $522 million to State Farm policyholders after the company manipulated the reports of adjusters and engineers to limit its responsibility.

The high court opinion dealt almost exclusively with the provisions of the federal False Claims Act that call for the existence of whistleblower lawsuits to remain secret for at least two months.

The sisters’ lawyer at the time, Dickie Scruggs, emailed information to reporters at The Associated Press, ABC News and The New York Times that revealed the lawsuit’s existence before the case was public, Kennedy wrote.

All three organizations published stories discussing fraud allegations, but none specifically mentioned the Rigsbys’ lawsuit. Scruggs later withdrew from the case, was subsequently convicted of trying to influence a judge in an unrelated case and was disbarred as an attorney.

The case is State Farm v. U.S., 15-513.