An official with the state attorney's office said on Thursday that gunmen had shot state police chief of detectives David Urquizo Molina.
About two hours later, authorities pursuing the suspected gunmen killed three people.
Three others were wounded and seven were arrested.
Footage from the scene shows those wounded being treated by paramedics.
Police also carried out searches on several vehicles in the neighbourhood.
Guerrero has been wracked with violence as competing drug cartels clash frequently with police and soldiers.