(CNN) -- Occupants of three trucks were working together in northern Mexico trying to pull over a vehicle carrying an American missionary before one of them shot the woman in the head, police said Thursday.
An autopsy detailed Thursday indicated that Nancy Davis, 59, died a day earlier from a single gunshot wound to the back of her head, according to a statement from Pharr, Texas, Police Chief Ruben Villescas, who is working with U.S. and Mexican authorities on the case.
Earlier, police said that Davis and her husband were traveling in a truck on a Mexican highway near the city of San Fernando, Mexico, when they were confronted by gunmen in a black pickup. San Fernando is south of the border city of Reynosa in Tamaulipas state.
On Thursday, Villescas added that the husband -- identified as Sam Davis by family friends -- told authorities "the men in the black truck were working with two light-colored trucks that paralleled them (and were) trying to pull them over," the Pharr police statement said.
"The gunmen were attempting to stop them and the victims accelerated in efforts of getting away from them," according to the earlier statement. "At a certain point the gunmen discharged a weapon at the victim's vehicle and a bullet struck the victim Nancy Shuman Davis on the head."
While noting they have not established a motive in this shooting, police pointed to past reports of "criminal organizations operating on Mexican roads ... targeting 4-door pickup trucks and ... SUVs."
Villescas said that authorities don't know which criminal group, if any, is responsible for Davis' murder.
In Wednesday's incident, at least one other gunshot hit the victim's vehicle, which is now in the custody of Pharr police.
After Davis was hit, her husband drove their truck "at high rate of speed" to the Pharr International Bridge, which crosses the Rio Grande. Nancy Davis was taken to a hospital in nearby McAllen, where she was pronounced dead about 90 minutes later.
The Texas Department of Public Safety, Immigration and Customs Enforcement, the FBI and U.S. Customs and Border Protection are also assisting, police said.
The Mexican Interior Ministry said it, too, was investigating "for the purpose of clarifying the facts and act accordingly to punish the person or persons responsible."
Merton Rundell, a professor in the missions department at Indiana's Union Bible College & Academy and a family friend, told CNN the couple had lived in Mexico since the 1970s and worked with the Gospel Proclaimers mission in Mexico.
Maryanne Wheeler, another friend who worked with the Davises in the 1990s, said Nancy Davis' death was a great loss.
"They breathed Mexico," Wheeler said. "That's their love.
"For 40 years she has gone around Mexico, trying to be there as a nurse, a friend, as a spiritual adviser and has loved them. They lost the best," she said. "They had a petite lady who had the tenacity of a bulldog and was there for you."
Wheeler said the couple had been shot at before and knew the dangers of the border area.
CNN's Sara Pratley, Anna Gonzalez and Nick Valencia and CNN Mexico's Krupskaia Alis contributed to this report