It happened in a second-floor bedroom at a residence on the 3100 block of North 28th Street, the department wrote. Authorities arrived on the scene around 7:45 a.m., they said.
The male victim, 39, was shot in the head and pronounced dead at the scene, police said. The woman, 43, was also shot in the head and taken to Temple Hospital where her condition remains critical, according to authorities.
The department said a weapon was recovered from the scene and that they will give updates as information becomes available.
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