WASHINGTON — There was nothing subtle about the ethnic slurs a juror in Colorado is reported to have made during deliberations over a Hispanic defendant charged with inappropriately touching teenage girls.

Two other jurors claim their colleague determined that defendant Miguel Angel Pena Rodriguez was guilty because Pena Rodriguez is “Mexican, and Mexican men take whatever they want.”

Now the Supreme Court will decide how to reconcile two tenets of the legal system that clash in Pena Rodriguez’s case: trial by an impartial jury and secrecy in jury deliberations.

The court is hearing argument Tuesday in Pena Rodriguez’s bid to upend his criminal conviction.

The Constitution guarantees criminal defendants a trial by an impartial jury. Secrecy in jury deliberations is an American legal principle that goes back more than 200 years.

The high court has resisted the call in earlier cases to examine what was said in the jury room. Secrecy, embodied in state and federal rules, is intended to promote the finality of a verdict and shield jurors from outside influences.

In Pena Rodriguez’s case, no other juror was alleged to have said anything improper and all 12 jurors, including the two who reported the inappropriate comments, voted to convict him.

In 2014, the justices unanimously reaffirmed the sanctity of jury deliberations. A motorcycle rider who lost a civil lawsuit over a grievous injury he suffered in a traffic accident sought a new trial. He based his claim on one juror’s report that a second juror said during deliberations that her daughter had been at fault in a similar case and a lawsuit against the daughter would have “ruined her life.”

Justice Sonia Sotomayor’s opinion in that case left open the possibility that some comments might go too far.

“There may be cases of juror bias so extreme that, almost by definition, the jury trial right has been abridged,” Sotomayor wrote in a footnote to her opinion.

After a jury convicted Pena Rodriguez of unlawful sexual contact and harassment involving teenage sisters at a Denver-area horse race track, two jurors provided his lawyer with sworn statements claiming that a third juror made derogatory remarks about Mexican men before voting guilty.

The jurors attributed several troublesome statements to the juror identified in court records by the initials H.C. He told the jurors that he used to be in law enforcement and where he used to patrol, “nine times out of 10 Mexican men were guilty of being aggressive toward women and young girls.” He also is said to have cast doubt on an alibi provided by a Hispanic witness for Pena Rodriguez because the witness was “an illegal.” The witness testified that he was in the country legally.

Pena Rodriguez’s case cries out for a strong message from the court in support of the right to a fair and impartial jury, his lawyers argued in court papers. “Barring defendants from introducing juror testimony recounting racially biased statements made during deliberations strikes at the heart of the Sixth Amendment’s impartial-jury guarantee,” they said.

Colorado, backed by 12 other states and the Obama administration, acknowledged that “racial bias is reprehensible and has no place in the jury room.”

But Colorado Attorney General Cynthia Coffman said this case is not the occasion for a ground-breaking ruling.

There are other ways to get at juror bias, the Obama administration said in a brief supporting Colorado. In one example given by the Justice Department, Pena Rodriguez’s lawyers did not question prospective jurors about prejudice, even after the judge cautioned lawyers that jurors in past cases “have been vocal in their dislike of people who aren’t in the country legally.”

Had the two complaining jurors spoken up sooner — before the jury reached a verdict — the judge could have investigated and replaced the juror, if necessary, without calling the whole trial into question.

The trial judge rejected defense lawyers’ bid to question the juror and that decision was upheld by split decisions in two Colorado appeals’ courts.

Civil rights groups including the NAACP Legal Defense and Educational Fund and the American Civil Liberties Union told the court that failing to consider the comments made by a juror identified only by the initials H.C. would have repercussions beyond Pena Rodriguez’s case.

A high court decision in favor of Colorado “would send an ominous signal that the American judiciary is, at best, indifferent to racial bias in jury verdicts,” the groups said.

A decision in Pena Rodriguez v. Colorado, 15-606, is expected by spring.