The incident occurred at an out-patient pharmacy in the Ben Taub General Hospital here where George Thomas Vallikkappil, 58, allegedly shot dead his woman colleague before turning the gun on himself on Wednesday.
While police did not name the woman victim, media reports said both hailed from Kerala.
Houston police said they are investigating the fatal shooting of a woman and a man in a murder/suicide incident at 1504 Taub Loop.
The identities of the female victim and male suspect are pending verification by the Harris County Institute of Forensic Sciences, they said.
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Houston police said the woman was in her work station behind the counter when Vallikappill walked up behind her and opened fire.
Moments later, he shot himself only a few feet away. Both were pronounced dead at the scene.
"The scene investigation and video surveillance revealed the male suspect shot the female, a co-worker, in the back and then shot himself," Houston Police Department (HPD) Homicide Division Senior Police Officer M Condon and Officer C Liu said in a statement.
The paper, quoting hospital officials, said they have no record of any complaints on file from Vallikappill or the woman. But, they said an internal investigation into the incident was on.
At Vallikappil's Southwest Houston home, his son Tom Vallikappil said: "We are 2 families suffering here."
"We're confused. We want answers. We don't have any answers," he was quoted as saying by ABC13.COM.
The outpatient pharmacy of Ben Taub General Hospital will remain closed until at least tomorrow, officials said.