The court, which was at full strength Tuesday with the return of Justice Ruth Bader Ginsburg, refused to hear the appeal from Kathrine May McKee. In doing so, it let stand a lower court decision that said she had no legal grounds to file a defamation suit because she's a limited public figure. She said in 2014 Cosby had raped her 30 years earlier. The suit said Cosby attorney Martin Singer repeatedly called her a liar in the press.
Cosby, 81, is serving three to 10 years in a Pennsylvania prison for the 2004 assault of a different woman.
The court also ruled Tuesday an intellectually challenged Texas man cannot receive the death penalty. A trial court came to the same conclusion in 2014 but the Texas Court of Criminal Appeals rejected it twice and upheld the death sentence pending a Supreme Court review.
The 85-year-old Ginsburg returned to the bench after spending the last several weeks recovering from lung cancer.
Ginsburg, appointed by President Bill Clinton, has attracted a cult following and gained a reputation as a reliably liberal voice during her time on the high court. Her role became more significant after President Donald Trump appointed two conservative justices to the court in the last two years -- swinging the balance so five of the nine justices lean toward the right. Trump has also appointed 30 federal appeals court judges, more than any other president at this point in their first term.
As for the cases the high court will hear, decisions could come as early as Wednesday.