A provincial official, Habeb-ul Rahman, also said the Afghans had died in an attack by US ground forces and aircraft.
A local policeman told the AFP news agency that he and some of his colleagues had gone to a part of the town where the US soldiers were involved in the early morning raid.
The policeman, who declined to give his name, said: "All of a sudden the Americans opened fire at us and immediately four policemen were killed including our chief.
"Helicopters then came to the area and fired into buildings."
The US military said the raid in Ghazni, about 100km south of Kabul, had been against Taliban fighters.
US major Chris Belcher, a spokesman for the US-led coalition, said the reports of the police deaths were being looked into.
Faced with troop shortages, US and Nato-led troops rely heavily on the use of airpower in their fight against the Taliban and other militants in Afghanistan.
Such tactics have caused many civilian casualties in past years, and at times caused friction with Afghan President Hamid Karzai, who has urged caution and co-ordination with Afghan authorities.
Negative public sentiment against US and Nato forces has built up after continued civilian deaths during foreign operations.
Aid agencies and Afghan officials have said that more than 500 civilians were killed by Western forces in Afghanistan last year, although US and Nato forces say the number of civilian deaths is lower.