a criminal. Mr. Radley also refused to send Boo to a mental asylum. "The sheriff hadn't the heart to put him in jail alongside Negroes, so Boo was locked in the courthouse basement" (11). The evidence clearly states that Boo did not go to jail, but to the courthouse basement instead. Due to mold in the basement and the cost to house Boo there, the county asked Mr. Radley to take him back after a while. So, no--Boo Radley never went to the county jail. If he had gone to jail it would have been after the scissors incident and not after the joyriding one. 

The above answers are not quite correct. Boo got in trouble because he got mixed up with the wrong crowd. He did not do anything horrible; he was just being a wild youth. Most importantly, he did not go to jail, even for a little.  Here is what the text says:

They did little, but enough to be discussed by the town and publicly warned from three pulpits: they hung around the barbershop; they rode the bus to Abbottsville on Sundays and went to the picture show; they attended dances at the county’s riverside gambling hell, the Dew-Drop Inn & Fishing Camp; they experimented with stumphole whiskey. Nobody in Maycomb had nerve enough to tell Mr. Radley that his boy was in with the wrong crowd.

One night, in an excessive spurt of high spirits, the boys backed around the square in a borrowed flivver, resisted arrest by Maycomb’s ancient beadle, Mr. Conner, and locked him in the courthouse outhouse.

The whole bit about Boo being in county jail was a rumor that Miss Stephanie perpetuated. She was the town gossip. 

Arthur Jr. had previously been jailed when he was still a teenager after getting into trouble with some of the Cunningham boys. While the other boys were sent to the state industrial school, Arthur's father got his son released to his own custody. He apparently locked Arthur Jr. away inside the Radley house, and "Mr. Radley's boy was not seen again for fifteen years." It was at this point that Boo, now 33 years old, ran into trouble again. He was led from the Radley house after he had suddenly plunged a pair of scissors into his father's leg. Afterward, Bo

... pulled them out, wiped them on his pants, and resumed his activities.  (Chapter 1)

But, "Boo wasn't crazy, he was high strung at times."

... he was not a criminal. The sheriff hadn't the heart to put him in jail alongside Negroes, so Boo was locked in the courthouse basement.  (Chapter 1)

Arthur's father soon had him out of the basement and back into Boo's own prison surrounded by the walls of the Radley house.

Arthur "Boo" Radley's father is a foot-washing Baptist and is known throughout the community as an austere, private man. As an adolescent, Boo Radley began to hang out with the Cunninghams from Old Sarum and ended up locking Mr. Conner in the courthouse outhouse. The boys were brought before a probate judge, who charged them with disorderly conduct and sent them to the state industrial school. However, Mr. Radley refused to send his son to the industrial school and kept him locked inside their home for some time. According to Miss Stephanie Crawford, Boo Radley also stabbed his father in the leg with a pair of scissors for no apparent reason when he was thirty-three years old. Mr. Radley refused to send his son to an asylum, and the sheriff kept Boo locked in the courthouse basement. Eventually, Mr. Radley took his son back home, and Boo remained reclusive from that day forward. Scout says,

Nobody knew what form of intimidation Mr. Radley employed to keep Boo out of sight, but Jem figured that Mr. Radley kept him chained to the bed most of the time (Lee, 11).

In chapter 5, Scout asks Miss Maudie about Boo Radley, and she tells Scout that Boo was always a well-behaved child. Maudie also admits that she does not know how or why Mr. Radley chose to keep his son secluded inside their home but recognizes that Boo must have suffered from staying indoors all the time.

Arthur (Boo) Radley seemed to be fairly normal growing up, according to Miss Maudie. When he was a teenager he became friends with some of the Cunninghams who were not a very good influence on him. Sometimes, too, guilt by association can get a kid into more trouble than he could think up on his own. In this case, the Cunninghams and Arthur were "in an excessive spurt of high spirits" one night, and they drove an old beat-up car backwards around the town square. When the officer, Mr. Connor, tried to arrest the boys, they locked him up in the courthouse outhouse. Nobody was hurt, but it sure made the officer embarrassed; so, he created a list of charges that include the following:

". . . so the boys came before the probate judge on charges of disorderly conduct, disturbing the peace, assault and battery, and using abusive and profane language in the presence and hearing of a female" (10).

The consequence was that the boys went to the state industrial school, which apparently was not something dishonorable. The boys actually got fed each day and received a quality secondary education. Unfortunately, Mr. Radley took his son Arthur home and promised there would never be any trouble out of him from then on. It seems that Arthur lost his freedom that day to a family warden that was worse than anything he would have experienced at the state school.

The initial event was that Arthur and his buds were just goofing off downtown, and ended up locking the town's beadle (law-man) in the courthouse outhouse.  Well, they were caught and brought before the judge, who sentenced them to

"the state industrial school, where boys were sometimes sent for no other reason than to provide them with food and decent shelter."

However, Mr. Radley thought that was a huge disgrace, and told the judge that if he released Arthur (Boo), then he "would see to it that Arthur gave no further trouble."  And, he did, because "Mr. Radley's boy was not seen again for fifteen years."  Then, after the alleged scissors-stabbing incident where Boo supposedly stabbed Mr. Radley with scissors in the leg, they locked him in the courthouse basement for a while until he went back to being a "malevolent ghost" in the Radley house.

According to Miss Stephanie Crawford--so take we should take this story with a grain of salt--when he was thirty-three years old, Arthur was sitting in the living room cutting clippings from The Maycomb Tribune to paste in his scrapbook when Mr. Radley walked by. Miss Stephanie said that Arthur "drove the scissors into his parent's leg, pulled them out, wiped them on his pants, and resumed his activities" (12). Mrs. Radley panicked and ran into the street screaming that "Arthur was killing them all." 

Someone suggested that Arthur be sent to an asylum over the incident, but Mr. Radley wouldn't hear of it. He agreed to have Arthur jailed, but the sheriff wouldn't jail him with African Americans, so Arthur was locked up in the courthouse basement instead.