The jury said a verdict had been reached on one of four charges against Castroneves' sports attorney Alan Miller and on one of seven charges against Castroneves' sister, who acts as his manager.
U.S. Judge Donald Graham said the verdicts would remain sealed until the jury can reach a decision on all the other counts. The jury has been deliberating since last Friday.
Castroneves faces one count of conspiracy and six counts of tax evasion from 1999 to 2004. He is accused of failing to report more than $5 million of income to the Internal Revenue Service.
Castroneves -- a popular member of the American open wheel auto racing series and a winner of the television show "Dancing with the Stars" -- faces 35 years in prison. He won the Indianapolis 500 in 2001 and 2002.
Duggar sisters unveil Christian dating rules in new book
McPhee, Cokas 'working on their marriage' after affair