WASHINGTON — The Supreme Court is refusing to overturn a $28.3 million verdict against R.J. Reynolds Tobacco in the first of about 8,000 lawsuits that have been filed against cigarette companies in Florida.

The high court today refused to hear appeals of a Pensacola, Fla., jury’s award to the family of Benny Martin, who died of lung cancer in 1995.

R.J. Reynolds lawyers argued that the case should be overturned because Florida judges aren’t making plaintiffs prove cigarette makers knowingly sold dangerous and defective products. People suing cigarette companies only have to prove addiction, and that their illnesses, or deaths of family members, were caused by cigarettes.

The cigarette company says that standard violates due process. But the Supreme Court — without comment — refused to hear their argument.