WASHINGTON (AP) _ The Supreme Court today refused to reduce a jury award of more than $11.2 million won from a tampon manufacturer by the family of a Kansas woman who died of toxic shock syndrome.

The court, without comment, rejected an appeal by Playtex Holdings Inc. seeking to reduce the award.

Playtex was sued by Kelly O'Gilvie, whose wife, Betty, died April 2, 1983.

His lawsuit charged that Mrs. O'Gilvie, a mother of two children, died from toxic shock syndrome caused by her use of Playtex super-absorbent tampons.

The company's warning on its package that ''tampons are associated with toxic shock syndrome'' was inadequate, the suit said.

A jury awarded actual damages of $1.5 million and punitive damages of $10 million. Playtex was ordered to pay 80 percent of the actual damage award and all of the punitive damages.

But a federal judge reduced the punitive-damages amount to $1.35 million on condition that Playtex withdraw its super-absorbent tampon from the market.

The 10th U.S. Circuit Court of Appeals overturned the judge's ruling in June 1987 and restored the full $10 million award.

The appeals court said, ''The record reveals abundant evidence that Playtex deliberately disregarded studies and medical reports linking high-absorbency tampon fibers with increased risk of toxic shock. There is evidence that Playtex deliberately sought to profit ... by advertising the effectiveness of its high-absorbency tampons when it knew other manufacturers were reducing the absorbency of their products.''

The appeals court also said the judge lacked adequate grounds to reduce the punitive award.

The reduction only would be proper if the judge found the award was ''so excessive that it shocks the judicial conscience,'' the appeals court said.

It said by lessening the judgment in return for Playtex' agreement to withdraw the high-absorbency tampons, the judge ''rewarded the company for continuing its (injury-causing) conduct long enough to to use it as bargaining chip.''

Toxic shock, caused by bacteria in the vaginal tract, was first linked to tampon use in the mid-1980s by the federal Center for Disease Control.

The case is Playtex Holdings vs. O'Gilvie, 87-1021.