* Brotherhood leader Badie denies use of violence
* Police vehicles torched in university protest
* Court hands life sentences to three Brotherhood members
* Leading secular activist referred to trial over protest (Updates with protest, activists)
By Tom Perry and Shadia Nasralla
CAIRO, Dec 9 (Reuters) - The Muslim Brotherhood's leader turned on his accusers on Monday when he appeared in court for the first time since he was arrested following the army's overthrow of Islamist President Mohamed Mursi.
"Why aren't you investigating the killing of my son, and the burning of my house and the group's offices?" Mohamed Badie asked of the judge, referring to his 38-year-old son killed in August, when the crackdown on the group was at its bloodiest.
Violence erupted again on Monday when police fired teargas at Mursi supporters protesting at Al-Azhar University, scene of frequent demonstrations against the army-backed government.
The protesters set ablaze three police vehicles, a witness said, and 58 students were arrested, an official said.
Badie, the Brotherhood's general guide, said the Islamist movement had perpetrated no violence, as his trial began at a police academy where Mursi went on trial last month. They were his first public remarks since his arrest on Aug. 20.
He faces charges that include inciting violence during a Brotherhood sit-in at Cairo University in mid-July.
The security forces have piled pressure on the Brotherhood, Egypt's best organised party, as the army-backed authorities advance a transition plan expected to yield presidential and parliamentary elections next year. The next step is a referendum on a new constitution, expected late this month or in January.
Since Mursi's fall, the government has verbally equated the Brotherhood with al Qaeda, accusing both of terrorism. The Brotherhood formally renounced violence decades ago.
Most Brotherhood leaders have been arrested since the army deposed Mursi on July 3 after mass protests against his rule. Mursi is accused of inciting the killing of protesters outside the presidential palace a year ago. His trial began on Nov. 4.
Badie appeared with Islamist politicians including Essam el-Erian and Mohamed el-Beltagi who are charged in the same case.
PRAYING WITH THE GENERALS
After the army toppled Mursi, Badie told supporters: "Our bare chests are stronger than bullets".
Mursi's removal opened the bloodiest chapter in Egypt's modern peacetime history. Security forces killed hundreds of his supporters, while some 200 soldiers and policemen have died, many in attacks by Islamist militants in the Sinai peninsula.
Badie's hearing was repeatedly interrupted by chanting from the cage where defendants appear in Egyptian courts.
"Down with military rule," shouted Beltagi, leading the others in chants against the generals whom the Brotherhood accuses of stealing power from a freely elected leader.
Reflecting on how Egypt's army commanders had turned against the Brotherhood, Badie said he had once prayed at the Saudi embassy in Cairo with the military council that ran the country until Mursi's election win in June 2012.
"Everybody respected the Brotherhood," he said.
An army source said Badie appeared to be referring to an event at the Saudi mission during the Islamic month of Ramadan. An army representative had attended, in line with protocol.
Badie's trial was adjourned until Feb. 11.
ACTIVIST SENT TO TRIAL
In Qalyubia province north of Cairo, a court sentenced three Brotherhood supporters to life in prison for attacking security forces, possessing firearms and terrorising citizens.
The Brotherhood, banned by a court ruling, has largely been driven underground, with thousands of its supporters arrested.
The government now plans to seize 62 private schools run by Brotherhood members, a state newspaper reported.
Criticism of the army-backed government has widened to secular activists in the last few weeks, following the passage of a new law that heavily restricts the right to protest.
The public prosecutor on Monday referred a leading online dissident to trial on charges including protesting without permission, an official in the prosecutor's office said.
Alaa Abdel Fattah, who was arrested on Nov. 28, was a symbol of the 2011 uprising against President Hosni Mubarak. He was referred to trial with 24 others, the official said.
The new protest law has deepened pro-democracy campaigners' concerns about the future of political freedoms in Egypt, where demonstrations were a rarity in Mubarak's days.
Strong Egypt, a party headed by former Brotherhood politician Abdel Moneim Abol Fotouh, urged Egyptians to vote against the constitution in the forthcoming referendum.
It cited reasons including expanded influence granted to the army in the constitution - another source of activist concern. (Reporting by Tom Perry, Mohamed Abdellah, Shadia Nasralla and Asma Alsharif; Writing by Tom Perry; Editing by Alistair Lyon)