In a March 19 ruling, a panel of the court sided with a Houston jury that decided in 2001 that Texas oil tycoon J. Howard Marshall never intended to leave any of his $1.6 billion estate to Smith.
Marshall's will gave most of his estate to his son, E. Pierce Marshall.
Smith had argued that her elderly husband had promised to leave her more than $300 million.
Smith died of a drug overdose in 2008.
