Investigators remained baffled Wednesday over a bizarre case in which twin sisters from Australia were mysteriously found at a shooting range south of Denver with gunshot wounds to the head.

They are trying to determine if it was a shootout, a failed murder-suicide or a suicide pact, while investigating why the 29-year-old sisters came to the U.S. on cultural exchange visas.

Complicating matters is the fact that investigators have had difficulty determining which sister died because they look so much alike. One sister was killed, and the other was upgraded Wednesday from critical to serious condition.

Authorities said the sisters were in the same lane at the Family Shooting Center and had at least two small-caliber pistols in their stall. Shooters at the range line up behind a wooden wall and shoot at targets through an opening that resembles a window, Arapahoe County sheriff's Capt. Louie Perea said.

Surveillance video at the range captured the sisters falling out of the stall about a half-second apart, with patrons quickly reacting, Perea said.

At least two shots were fired, Perea said. He declined to release further details, citing the ongoing investigation.

No suicide note was found and a search of the twins' luggage at a nearby hotel revealed nothing about what happened, Perea said. There was no apparent indication of a dispute between the sisters, or any indication they were shot by somebody else. No suspects were being sought.

"We want to be open-minded and make sure we're doing a thorough investigation," Perea said. "We're still trying to track the days leading up to the incident."

Perea said the sisters had visited the shooting range at Cherry Creek State Park in Aurora at least twice before the fatal shooting.

Investigators initially couldn't determine which woman had died. But they now believe they know, "based on reasons that are not scientific," said Dr. Kelly Lear-Kaul, a forensic pathologist and deputy with the Arapahoe County Coroner's Office.

They were working with the Australian consulate in Los Angeles to obtain fingerprints or dental records to positively identify the two. Perea said the U.S. Immigration and Customs Enforcement had also been contacted because the two submitted fingerprints for their visas.

Authorities won't release either sister's name until they have been positively identified, Perea said.

Perea said authorities attempted to interview the surviving twin after her condition was upgraded, "but she was still heavily medicated,"

"The interview was ineffective. We won't try to interview her until early (Thursday) morning," he added.

Australia's Department of Foreign Affairs and Trade said in a statement the twins were from Victoria state in southeast Australia. The Australian consulate in Los Angeles was working closely with Colorado authorities, said Scott Bolitho of the Australian Embassy in Washington, D.C.

Both women were in the United States on cultural exchange visas, with one sister arriving in the U.S. on Aug. 19 and the other on Sept. 7. One sister was due to return to Australia on Tuesday, Perea said.

It's not clear what the women were doing in the United States. Perea said no one has come forward to say they knew the sisters, acknowledging that they haven't been publicly identified yet.

Cultural visas are issued for up to 16 months for a range of purposes from travel to working as an au pair, said Tim Counts of U.S. Bureau of Citizenship and Immigration Services. Holders must be sponsored by an organization and be involved in some activity that involves their culture or language, he said.

Perea said the family was arranging Wednesday to travel to the United States, backing away from an earlier statement that the family was en route. During a brief conversation with investigators, family members shed no light on what may have happened, Perea said.

"We didn't get into specifics. Obviously they're mourning the loss of one daughter and the wounding of another," he said.

Shooting range owner Doug Hamilton was not at the range Wednesday and had not returned repeated messages left by The Associated Press.

(This version corrects date of arrival to Sept. 7, not 17.)