But interviews with parents of three of the children, and remarks from the American Civil Liberties Union of Tennessee, which is investigating the episode, raised questions about the conduct of the police and their handling of juvenile students.

Other high-profile cases have recently occurred at schools in Texas and in South Carolina.

“It is wholly unacceptable to haul children away from school in handcuffs for a charge that does not actually exist,” Hedy Weinberg, executive director of the A.C.L.U. in Tennessee, said in an email. “The growing trend of criminalizing students — particularly students of color — within our educational system must stop.”

The A.C.L.U. said the charge of criminal responsibility for the conduct of another could be used only when there was an accompanying criminal charge that a person is accused of facilitating.

The A.C.L.U. said it was aware of at least 10 children who were arrested in the Murfreesboro case.

Zacchaeus and LaVonia Crawford, who identified themselves as the parents of three of them, said in interviews that a day before the arrests, a police officer went to their home and asked whether they knew anything about the boy who was pushed and hit in the video, and showed them a screen shot. During the visit, they said, the officer also asked for their children’s names.

“They came across some evidence that he might have been harmed,” Ms. Crawford said. “My being a mother, I tried to tell her, as well as my children tried, to identify the boy.” She said she and her children provided their own names, told the officer where they thought the boy lived, and the officer left.

The next day, the Crawfords were told by the principal and a police officer that their 10-year-old daughter had been arrested and was being taken to the county juvenile center. The officer said that a warrant had been signed and that their 9-year-old son was also named on it.

When the parents arrived at the center, taking their son, they discovered that their 11-year-old daughter was there, as well. She had been taken out of class and handcuffed, Mr. Crawford said.