The battle last week in Guadalajara resulted in the deaths of three policemen and four cartel members.
A Justice Department report obtained by CBS says one of the grenades used in the clash is connected to Jean Baptiste Kingery, an alleged arms trafficker.
U.S. officials have allowed Kingery to operate for years despite what the network called "significant evidence" he had sold large numbers of grenade parts and ammunition to the cartels, CBS reported Thursday.
Documents indicate agents with the Bureau of Alcohol, Tobacco, Firearms and Explosives began watching Kingery in 2004 for allegedly trafficking AK-47s into Mexico. In 2007, ATF reported he was dealing in grenades.
CBS said the U.S. Attorney and ATF office in Arizona developed a plan to allow Kingery to move grenade parts into Mexico and follow them to his factory. That plan failed after they lost track of him.
U.S. authorities detained Kingery in 2010 when he tried to smuggle grenade bodies and ammunition into Mexico. He was released after prosecutors said they didn't have a strong case against him.
In 2011, Mexican authorities raided his factory and arrested him. Police said he confessed to training cartel members how to build grenades.
ATF said Wednesday it had no information about Kingery's connection to the grenade used last week, CBS reported.
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