"We don't have all of the information, and we haven't drawn any conclusions," Nash said.
He said he didn't know how many family members were camping or where they are from in Idaho. Names haven't been released.
A federal law went into effect Feb. 22, 2010, allowing visitors to possess firearms in the park. Nash said records show two shooting deaths occurred in the park in 1978, but he didn't have details.
"Given the 3 million visitors we see here every year, there thankfully are very few fatalities reported in the park," Nash said. He said heart attacks were the primary cause of human deaths in the park.
The park recently reported that through August, about 2.5 million people have visited the park.
Portions of the park are within the borders of Wyoming, Idaho and Montana, with the girl's death occurring in Wyoming. Nash said park authorities have exclusive federal jurisdiction because the park predates the formation of those states, but works with surrounding law enforcement agencies. That means park rangers and special park agents are leading the investigation, he said.
The park has a federal district court, a federal magistrate, and an assistant U.S. attorney based in Mammoth Hot Springs, Nash said.
Visitation to the park starts winding down this time of year, but is also favored by some for that reason, as well as the opportunity to see bugling bull elk as well as other wildlife that can be more visible in cooler weather.