After shots rang out in Dealey Plaza, the presidential motorcade sped north on Stemmons
Freeway toward Parkland Memorial Hospital.
Roy Kellerman, who was riding in the front seat of the president's limousine, used his radio to alert the lead car in the motorcade that the president had been shot and that they were headed to the hospital. Dallas Chief of Police Jesse E. Curry, and officers on motorcycles, led the president's car to Parkland while Curry ordered the hospital to be put on notice of the president's arrival.†
According to the Warren Report, "the radio log of the Dallas Police Department shows that at 12:30 p.m. on November 22 Chief Curry radioed, 'Go to the hospital--Parkland Hospital. Have them stand by.' A moment later Curry added, 'Looks like the President has been hit. Have Parkland stand by.'"
Meanwhile, at the Texas School Book Depository, Dallas police officer M.L. Baker ran into the building after hearing what he believed was a high-powered rifle being shot from a high floor.†
"It sounded high and I immediately kind of looked up, and I had a feeling that it came from the building, either right in front of me [the Depository Building] or of the one across to the right of it," Baker told the Warren Commission.
In the lobby of the book depository, Baker said building superintendent Roy Truly led him up the stairs. On the second floor, Baker recalled running into a man, later determined to be Lee Harvey Oswald, in the lunchroom near the vestibule. Baker said that the man seemed calm, was breathing normally and didn't say a word to him or change his expression. Truly found the reaction unusual given the circumstances, but did confirm to Baker that the man worked in the depository.†
"He didn't seem to be excited or overly afraid or anything. He might have been a bit startled, like I might have been if somebody confronted me. But I cannot recall any change in expression of any kind on his face," Truly told the Warren Commission.
Truly and Baker eventually climbed all the way to the 7th floor and the roof, where they spent several minutes looking around.
The Warren Commission estimates Oswald left the book depository at about 12:33 p.m., though his absence wasn't noticed until about a half-hour later when Truly noticed that Oswald was not among the employees being questioned by police. He then retrieved Oswald's personal information from his employee application card and delivered it to Capt. Will Fritz, who would soon find the rifle on the sixth floor.
†Source: Archives.gov - Oswald's Actions in Building After Assassination