(CNN) --Authorities have not said whether the victims' sexual orientation played a part in the shooting, but the police chief of the town said the incident did not appear to be a random attack.
"This particular case, it does have some of the earmarks of a targeted attack," Chief Randy Wright of Portland told local station KZTV.
One of the victims died, while the other is clinging to life.
"Well, at best we know they were really good friends. Some of their friends have stated that they were in a relationship," Wright told CNN on Monday night. "They were found by two visitors to the park Saturday morning."
Murders are not common in the town of about 16,000, just north of Corpus Christi. The last took place two years ago, Wright said.
In latest incident, the women were found in an observation platform of an overlook at a park, the police chief said.
Authorities believe they were shot sometime late Friday night or early Saturday morning.
One of the victims, 19-year-old Mollie Olgin, was pronounced dead after the shooting.
The second, Mary Kristene Chapa, 18, was in serious condition at a local hospital with a gunshot wound to the head.
"We have not been able to take a formal statement from Chapa as she is receiving medical care," Wright said.
Witnesses told police they saw a dark-colored vehicle leaving the scene. But beyond that, detectives have little to go on.
Asked if police were looking at a hate crime, Wright said the case was being investigated "as a murder."
"I've been trying to think of anybody I know that would try and hurt them for any reason - especially them being a couple," Samantha Garrett, Olgin's roommate, told KZTV. "And not one person has ever come to mind."