American Experience . Oswald's Ghost | PBS
On April 10, 1963, someone tried to kill a former Army general, Dallas resident Edwin A. Walker, who was making his name as a controversial right-winger. In early December 1963, while investigating the Kennedy assassination, the FBI determined Oswald had fired the shots at Walker.
Walker held extreme political views, accusing a variety of Democrats of being "pink" Communist sympathizers and opposing the integration of Southern schools. After Attorney General Robert Kennedy issued a warrant for Walker's arrest, the general declared himself a "political prisoner" of the Kennedy administration.
Oswald's motivation to kill Walker is explained in the Warren Commission report:
"[Marina Oswald] testified that Oswald said that General Walker 'was a very bad man, that he was a fascist, that he was the leader of a fascist organization, and when I said that even though all of that might be true, just the same he had no right to take his life, he said if someone had killed [Adolf] Hitler in time it would have saved many lives.'"
The note below, translated from Russian, was delivered to investigators along with some of Oswald's books. Marina Oswald would later testify that her husband had attempted to kill Walker and had left her this note at that time, detailing what she should do if he did not return.
Go to the link at the top of this post and anyone can read Oswald's note at the bottom of that webpage. He implicated himself according to his note verified by his wife.
11. If I am alive and taken prisoner, the city jail is located at the end of the bridge through which we always passed on going to the city (right in the beginning of the city after crossing the bridge).
source: Warren Commission Report, "Chapter 4: The Assassin. Prior Attempt to Kill: The Attempt on the Life of Maj. Gen. Edwin A. Walker." pp. 183-184. Chapter 4