By Lawrence Hurley

WASHINGTON (Reuters) - The role of race in the U.S. criminal justice system came before the Supreme Court again on Tuesday in a case in which a Hispanic man is seeking to overturn his sexual offense convictions due to a juror's racially charged statements during deliberations.

Several justices appeared sympathetic to the arguments made by lawyers for Miguel Pena Rodriguez, who was convicted after being accused of sexually groping two teenage girls in a bathroom in 2007 at a Colorado race track where he worked.

At issue is whether racially biased statements violate a defendant’s right to a fair trial under the U.S. Constitution’s Sixth Amendment. Prosecutors cite a long-standing legal tradition of jury deliberations generally remaining off-limits in any attempt to overturn a verdict.

Other jurors said one juror in the case, a former law enforcement officer, stated during deliberations that the defendant "did it because he's Mexican, and Mexican men take whatever they want."

The juror also called the defendant an "illegal" despite the fact that Pena Rodriguez, originally from Mexico, was a legal permanent U.S. resident.

Conservative justices John Roberts and Samuel Alito appeared concerned about setting a precedent that opens the door to complaints about juror conduct not just on racial bias but on other forms of discrimination, including religion and sexual identity, or just objectionable conduct in general.

"What do you say to the defendant who is going to be spending the rest of his life in prison as a result of the jury verdict that was determined by flipping a coin?" Alito asked.

Liberal Elena Kagan said that in U.S. legal history race has often been treated differently than other forms of bias.

"We have the best smoking-gun evidence you're ever going to see about race bias in the jury room," Kagan said.

Conservative Anthony Kennedy, who often casts the deciding vote in close cases, could determine the outcome. He appeared particularly concerned about racial bias in death penalty cases.

Kennedy said prosecutors appeared to be arguing that "the more insidious the evil" committed by a juror during deliberations, the less reason there is to investigate whether a defendant has been denied a fair trial.

Pena Rodriguez, convicted of three misdemeanors, said he was wrongly accused. He was sentenced to two years of probation and had to register as a sex offender.

The Colorado Supreme Court rejected Pena Rodriguez's request for a new trial last year.

Another racially-tinged case before the court last week involved whether a black Texas death row inmate should get a new sentencing hearing after his own lawyer called an expert witness who testified the defendant was more likely to be dangerous in the future because of his race.