In 1961 Jim Garrison ran for District Attorney, winning against incumbent Richard Dowling by 6000 votes in a five-man race. Despite lack of major political backing, his performance in a televised debate and last minute television commercials are credited with his victory.

He attacked the police. Superintendent of Police Giarrusso challenged Garrison's legitimacy, claiming, "the DA is trying to run the police department."

Garrison charged nine policemen with brutality, but dropped the charges two weeks later. At a press conference he accused the state parole board of accepting bribes, but could obtain no indictments. He accused the state legislature of the same, but held no investigation. He was unanimously censured by the legislature.
In 1965, he ran for reelection against Judge Malcolm O'Hara, who charged Garrison with a "Napoleonic complex" and said his "ugly force...compells him to destroy everyone who fails to bow to his will." Garrison won with 60 percent of the vote.
In 1973 he lost the office to Harry Connick, Sr. After Harry, the next DA of New Orleans is Eddie Jordan. so you only have to count back three guys to get to 1961.
I think Mr. Jordan has some thoughts about Clay Shaw's involvement in the Kennedy assc. but he ain't saying. (thank you Wikipedia, the free encyclopedia, for most of the text and thank you Eddie Jordan's office lady for taking the picture)