Two Iraqi policemen were badly wounded and US occupation forces arrested six of their comrades after the overnight battle, police Colonel Farhat Qadir said on Friday.
"The battle happened by mistake," he said, declining to elaborate.
The police in Kirkuk have previously been targets of anti-government forces in the area.
US forces maintain bases in the northern city, which is an important centre of oil production.
The city's Arab, Kurdish and Turkmen populations claim rival historical property rights that have caused sporadic violence in Kirkuk since Saddam Hussein was toppled last year.