The shooting occurred around 8pm in Plano, less than 20 miles (32km) northeast of Dallas.
"The first responding officer actually heard gunshots taking place inside the residence", police spokesman David Tilley said. The assailant was shot and killed by a Plano police officer while the rampage was still unfolding.
Two others who have been injured in the shooting have been taken to the local hospital.
"We're looking into a motive", Tilley said, adding that the relationship between the victims and the shooter was unknown as yet.
Rushin would not confirm the shooter's identity or that it was a domestic-violence homicide, but he used numerous key words that typically come up in such an investigation.
When the officer entered the home, he saw several victims inside as well. All the people who died in the shooting were adults in their 20s and 30s and the victims were of both genders, Rushin said.
New Hampshire hospital locked down after report of active shooter
One person is in custody after an active-shooter report at a New Hampshire hospital, according to the city's website . The hospital was under lockdown and it wasn't clear if that was lifted.
"I'm anxious", she told the newspaper.
Police said they've never seen an incident of this magnitude in Plano and neighbors are in shock. The officer who shot the suspect was placed on administrative leave pending the investigation, which is protocol, he said. After police arrived on scene, Glover heard officers yelling, "Hands up", before the spraying of more gunfire was heard.
"I truly wish we knew who alternate casualties were".
"They argued and you could hear it getting really, really loud", the witness said.
"We're trying to put all the puzzle pieces together", Tilley said.