Henderson police spokesman Shane Lewis said the 81-year-old Armour was found dead at his Henderson home about 3:30 p.m. Sunday with a gunshot to the head.
A Clark County coroner's office spokeswoman said Monday the case had been ruled a suicide.
Ann Lynch, a Sunrise Hospital and Medical Center spokeswoman and family friend, said Armour had been in declining health in recent years.
Armour's father, known as 'The Silver Scot,' was born in Scotland and was the first to represent both the United States and Britain in international play. He won the U.S. Open in 1927, the PGA Championship in 1930 and the British Open in 1931. He was elected to golf's Hall of Fame in 1942.
Armour's son, Tommy Armour III, 43, won the Phoenix Open in 1990.
Dr. Armour joined the Sunrise Hospital staff in 1964, and served as a hospital trustee in the early 1980s. He retired in 1997.
Lynch said a funeral had not been scheduled.
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