There is no shred of actual evidence of this, just anecdotes. For what it is worth none of the witnesses reported seeing them act acquainted. As Oswald was walking away he said "poor d__n cop" or "poor dumb cop". If he had shot someone he knew, he probably would have referred to him in a less generic fashion.
J.D. Tippit was killed by Lee Harvey Oswald, who was a suspect in the assassination of President John F. Kennedy. It is believed that Tippit was shot because Oswald panicked and needed to avoid capture by the police.
J. D. Tippit
The Warren Commission believed that it was Lee Harvey Oswald.
Yes, within hours of the Kennedy assassination he killed a police officer called J. D. Tippit. He was soon arrested for the shooting and quickly suspected of being involved in the murder of President Kennedy.
J. D. Tippit
Lee Harvey Oswald (acting alone) shot and murdered President John F. Kennedy and Dallas Texas police officer J.D. Tippit. Jack Ruby (who was mentally unstable) shot and killed Oswald, while Oswald was in police custody. Ruby died of cancer in prison.
Lee Harvey Oswald shot Kennedy; Jack Ruby later shot Oswald.
The Warren Commission Report claimed Lee Harvey Oswald shot and killed Dallas Police Officer J. D. Tippit.
The officer that John F. Kennedy's shooter killed was Dallas Police Department officer J.D. Tippit. Tippit was shot and killed by Lee Harvey Oswald approximately 45 minutes after the assassination of President Kennedy.
Oswald
Oswald was shot by jack ruby
After assassinating President John F. Kennedy, Lee Harvey Oswald left his rooming house in Dallas, Texas, with the intention of going to his friend's house. Oswald wanted to retrieve a gun and money before taking a bus to Mexico. However, he was intercepted by police while walking on the street and ultimately arrested.