you said Peter Finch, you're off by almost 40 years.
Sidney Howard was killed in a tractor accident on his farm in 1939, months before the
film of his
Oscar-winning screenplay for Gone With The Wind appeared on the
screen. He had been previously nominated for Arrowsmith (1931/32) and Dodsworth (1936), and had won the 1925 Pulitzer Prize for Drama for his play They Knew What they Wanted. With his posthumous Oscar for GWTW, he became the first person to have won both the Pultizer Prize and the Academy Award.
The first Oscar winner to die was Joseph Farnum, who won the only award ever presented for Title Writing at the first banquet at the Hollywood Roosevelt Hotel on May 16, 1929. He passed away on June 2, 1931 at the age of 46.