Houston police said the woman was in bad shape.
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Investigators said one rifle round came through the wall of her apartment on Dashwood Drive near Renwick and Bellaire in southwest Houston just before 2 a.m. Wednesday.
Police believe it was a drive-by shooting.
The 26-year-old woman was shot in the shoulder as she slept, investigators said. Several rifle shell casings were found in the parking lot.
It was unclear exactly how many shots were fired.
Investigators believe someone drove by the apartment and fired several shots into the downstairs area. The woman was reportedly sleeping near a window in the living room.
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"Our complainant was in a makeshift bedroom-type area in the downstairs. One of the rounds went through the wall and hit her in the shoulder," Lt. R. Willkens said. "She is in bad shape. Like I said, it was rifle rounds."
The woman was taken to a hospital in serious condition, though police said she was conscious and breathing.
Police said there was a man inside the apartment at the time of the shooting, but he was not hurt.
The man lives at the apartment and the woman was just visiting, officials said.
Investigators did not provide details on a suspect or vehicle description.
They said the man and woman told them they have no idea why anyone would do this.
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