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Officials said at about 1:16 p.m., officers with the League City Police Department were called by a man, David Varley, who said his wife had been injured.
When officers arrived at the South Shore Lakes Apartments at 3850 FM 518, his wife was found dead due to an apparent gunshot wound.
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From there, officers began an investigation and collected evidence. A short time later, Varley was taken into custody.
Varley's bond was set at $250,000 by the Galveston County District Attorney's Office.
The name of the woman was not immediately made known.