Jurors weighing how to punish Johnson & Johnson in a lawsuit asked a judge if they could force the company to warn consumers that its Johnson’s Baby Powder could be contaminated with asbestos, according to the law firm that won the case against the health-care giant.

After the judge said no, the jury awarded $4 million in punitive damages Thursday to Joanne Anderson, a 68-year-old woman who claimed her deadly cancer was caused by asbestos in J&J’s baby powder. A day earlier the jury had awarded $21.7 million to Anderson, finding J&J 67 percent responsible for her mesothelioma.

The court wouldn’t have the power to order a company to add or change warnings on its products, said David Logan, law professor at Roger Williams University in Bristol, Rhode Island. “It’s not a remedy that can be ordered in a damages action,” he said.

The fact that the jury asked the question at all, however, “is a bad sign for J&J,” said law professor Carl Tobias of the University of Richmond in Virginia. “That should make J&J wake up if that’s the way juries are looking at these cases.”

J&J is facing thousands of lawsuits alleging its talc products are connected to cancer, primarily ovarian, but with a growing number claiming asbestos-related mesothelioma. The suits center on the claim that the company failed to warn of risks.

“It helps the plaintiffs’ cases if jurors are taking that kind of perspective,” said Tobias. The jurors in Anderson, he said, “believe it needs a warning.”

Carol Goodrich, a spokeswoman for J&J, didn’t immediately comment on the juror question. J&J talc products don’t contain asbestos or cause mesothelioma, she said after the verdict. The company has also rejected any connection between its talc products and ovarian cancer. J&J will appeal.

The jury query was highlighted in the press release issued by Anderson’s lawyers at Simon Greenstone Panatier. “The question shows that the jury understood that J&J knew about the danger of asbestos in their baby powder and chose to do nothing,” David Greenstone, an attorney for the plaintiffs, said Thursday in an email.

After the verdict, jurors outside the courtroom cited a 1969 company document related to “project code 101,” in which J&J doctors warned of the risk of asbestos in talc, and possible litigation in the future.

One juror who asked not to be identified said the evidence showed that J&J knew it had a problem in 1969 and kept marketing its baby powder. He said he advocated for a bigger damages award.

The case is Anderson v. Borg Warner Corp., BC 666513, California Superior Court, Los Angeles County (West Covina).