One man blew himself up in a classroom, reports CBS News correspondent Kimberly Dozier. The second hit a bomb shelter where panicked students had run to hide.
The bombing came as claiming to have kidnapped a U.S. security consultant — the seventh Westerner abducted in Iraq since Nov. 26 — and the U.S. military reported another American soldier killed in a roadside bombing in Baghdad.
Late Tuesday, another suicide bomber blew himself up in a cafe frequented by police in a Shiite neighborhood in Baghdad, killing three people and wounding 20, police said. One of the dead and three of the wounded were policemen, officials said.
The violence came as continued in Baghdad, with the ousted leader defiantly telling the judges to "go to hell" and vowing not to return to court Wednesday.
The assault on the police academy was carefully planned to maximize casualties, all of whom were police officers or cadets.
The first bomber struck near a group of students outside a classroom, a U.S. military statement said.
Thinking they were under mortar fire, survivors rushed to a bunker "where the second bomber detonated his vest," the statement added. One of the wounded was an American contractor.
"We were sitting in the yard when we heard an explosion," said police Maj. Wisam al-Heyali. "Seconds later, we were hit by another explosion as we were running. I saw some of my colleagues falling down and I felt my hand hit, but I kept on running."
A statement on an Islamist Web site in the name of al Qaeda in Iraq said "two blessed brothers" staged the attack on the academy, "which continues to produce the dogs that shed the blood and violate the honor of Sunni Muslims."
The claim's authenticity could not be independently verified, but al Qaeda in Iraq's leader, Abu Musab al-Zarqawi, has often denounced Shiites because of religious differences and their leading role in the U.S.-backed government.
Iraqi police also said the attackers may have been policemen or students, fresh evidence that insurgents have infiltrated the country's Shiite-dominated security forces. President Bush has linked an eventual U.S. troop withdrawal to the ability of Iraq's army and police to combat the insurgents.
The attack was the deadliest against Iraqi security forces since Feb. 28, when a suicide car bomber struck a crowd of mostly Shiite police and army recruits in Hillah, killing 125. In September, at least 88 people were killed in a suicide car bombing in a heavily Shiite neighborhood of Baghdad.
U.S. and Iraqi officials have warned of an increase in insurgent attacks ahead of the Dec. 15 elections. Ramadi residents reported seeing fliers Tuesday in the name of al Qaeda in Iraq warning people not to vote and threatening to bomb polling stations.
Police Capt. Jalil Abdul-Qadir said 43 people were killed, including seven policewomen, and at least 73 wounded in the attack on the academy. U.S. forces said the death toll was at least 27.