The twin blast in, a Sunni-dominated town about 12 miles (20 kilometers) from the Iraqi capital, were the latest in a series of attacks across Iraq.
They came at a time of public debate over whether to ask the United States to keep some American troops here past their year-end withdrawal deadline from the country.
"It was awful some of the lightly wounded people were running in all directions, either crying or screaming for help," a policeman who identified himself only by his nickname, Abu Haider, said at the scene. He said he was not authorised to give his full name.
Burned bodies were lying on the ground and about 20 cars were on fire, witnesses said.
The assailants first detonated the around noon in the parking lot of Taji's local council building, police said. When civilians and security forces rushed to the scene to help the victims, the second bomb was detonated.
The later sealed off the area, and at one point four ambulance were seen waiting for permission to evacuate the wounded.
A doctor at Kazimiyah Hospital outside Baghdad who saw the bodies confirmed the casualty figures. He spoke on condition of anonymity because he was not authorised to brief the media.
Maj Gen Qassim al-Moussawi, a spokesman for Baghdad's military operations command, gave a lower count, saying 27 were killed and 50 wounded.