The exchange of gunfire took place in the farming community of La Concepcion, just south of Acapulco, after elements of the community police detailed a young man for disorderly conduct during town festivities early Sunday morning.
Eight local residents were killed in that exchange.
After Army soldiers and state police later moved into the town, three members of the community police were shot dead after resisting them, Roberto Alvarez, a state security official, told reporters.
Another 30 members of the local police, which had been authorized by state officials to operate in the small town, were arrested in the operation.
Acapulco is the biggest city in the southern state of Guerrero, one of Mexico's most lawless and a center of opium poppy production.
Violence in the state has also been fed by turf wars over the distribution of drugs like cocaine and methamphetamine.
The beach resort is one of Mexico's most famous and for decades served as a playground for Hollywood stars.
In recent years, however, Acapulco has been roiled by vicious gang warfare and is now ranked one of the most murderous cities in the world.
