This is from the famous compilation of Oswald statements by Mae Brussells. It shows that Oswald denied going to Mexico City, saying that he had only been to Tijuana.
2:25 - 4:04 P.M. Interrogation of Oswald, Office of Capt Will Fritz
"My name is Lee Harvey Oswald. . . . I work at the Texas School Book Depository Building. . . . I lived in Minsk and in Moscow. . . . I worked in a factory. . . . I liked everything over there except the weather. . . . I have a wife and some children. . . . My residence is 1026 North Beckley, Dallas, Tex." Oswald recognized FBI agent James Hosty and said, "You have been at my home two or three times talking to my wife. I don't appreciate your coming out there when I was not there. . . . I was never in Mexico City. I have been to Tijuana. . . . Please take the handcuffs from behind me, behind my back. . . . I observed a rifle in the Texas School Book Depository where I work, on Nov. 20, 1963. . . . Mr. Roy Truly, the supervisor, displayed the rifle to individuals in his office on the first floor. . . . I never owned a rifle myself. . . . I resided in the Soviet Union for three years, where I have many friends and relatives of my wife. . . . I was secretary of the Fair Play for Cuba Committee in New Orleans a few months ago. . . . While in the Marines, I received an award for marksmanship as a member of the U.S. Marine Corps. . . . While living on Beckley Street, I used the name 0. H. Lee. . . . I was present in the Texas School Book Depository Building, I have been employed there since Oct. 15, 1963. . . As a laborer, I have access to the entire building. . . . My usual place of work is on the first floor. However, I frequently use the fourth, fifth, sixth, seventh floors to get books. I was on all floors this morning. . . . Because of all the confusion, I figured there would be no work performed that afternoon so I decided to go home. . . . I changed my clothing and went to a movie. . . . I carried a pistol with me to the movie because I felt like it, for no other reason. . . . I fought the Dallas Police who arrested me in the movie theater where I received a cut and a bump. . . . I didn't shoot Pres. John F. Kennedy or Officer J. D. Tippit. . . . An officer struck me, causing the marks on my left eye, after I had struck him. . . . I just had them in there," when asked why he had bullets in his pocket.