Police spokeswoman Jodi Silva says the husband, whose name hasn't been released, died Monday at another hospital.
A spokesman for Houston Methodist Willowbrook Hospital, where the shooting happened Sunday afternoon, didn't immediately comment.
Silva says the woman gave birth around 1:30 p.m. Sunday. Police say the husband and wife were in her room hours later when he pulled a gun and shot himself.
The wife wasn't hurt. Silva had no details on the gender of the baby, who wasn't in the room during the incident.
Further details weren't immediately available.
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