The shooting of 29-year-old twin sisters Monday at an Arapahoe County gun range continues to puzzle investigators, and their family in Australia still doesn’t know which sister is dead.

The Australian Department of Foreign Affairs and Trade located the family in Victoria state in southeast Australia Tuesday evening. Because the women look the same, Arapahoe County authorities are not sure which one was killed.

Both women were shot in the head, one of them dying instantly.

The other was in critical but stable condition Tuesday night at Swedish Medical Center in Englewood, unable to talk to investigators or shed any light on the mystery.

The Arapahoe County Coroner’s Office won’t release their names until the identity of the dead woman is confirmed through dental records, tattoos, scars or other distinguishing marks.

Investigators still don’t know whether the shooting was an accident, a suicide or foul play. No suicide note was found.

“Every time I get new information there’s a new twist,” sheriff’s Capt. Louie Perea said. “We’re keeping an open mind.”

Investigators have ruled out the possibility that a third person could have shot them.

A surveillance video at the Family Shooting Center in Cherry Creek State Park showed both women falling backwards to the ground almost simultaneously outside the shooting stall about 2:50 p.m. Monday.

The video did not show what happened inside the stall, however. No one entered or left the stall other than the two women.

The women had been to the shooting range before and knew how to use the pistols they had rented, said Doug Hamilton, the gun range’s owner. He would not say when they were there previously.

One of the sisters had been scheduled to fly home to Australia on Tuesday, Perea said.

One had been in the United States since Aug. 17 and the other since Sept. 19, according to their cultural-exchange visas, which often indicate participation in an educational travel program.

Their reason for being in Colorado is not known.

They had stayed at the La Quinta Inn & Suites in the Denver Tech Center, about 5 miles away, for several days until Friday, Perea said.

The pair took a cab to the range. The driver told investigators he didn’t notice anything unusual, Perea said.

Neither did other people using the range when the shooting happened. The women were at the range for an hour and 20 minutes beforehand.

“They were interacting with each other, and nothing seemed unusual,” Perea said. “They were just a couple of gals having fun at the range.”

Suicides have occurred at the Family Shooting Center, one in 2004 and one last year, Hamilton said.

Joey Bunch: 303-954-1174

or jbunch@denverpost.com