A teenage girl was arrested on suspicion of inciting religious hatred after allegedly burning an English language version of the Koran, police said.
The 15-year-old was questioned and bailed by detectives last Friday after the alleged incident at a school in the Sandwell area of the West Midlands.
She is alleged to have posted footage of the burning booklet on Facebook.
A 14-year-old boy was arrested on Tuesday on suspicion of making threats on the social networking site, in connection with the alleged incident. He was released on bail, a spokeswoman for West Midlands Police said.
She added: "The local neighbourhood team have strong links with the school and have been working closely with key partners from the community and the local authority to resolve the matter locally.
"West Midlands Police will investigate and monitor any crime reported by individuals who may have been targeted because of their disability, gender, race, religion or belief, sexual orientation or transgender."