Investigators said the officer drove his Dodge truck through the side of a home in the 11300 block of Brownfield Road, knocking the two people out of bed on Friday, April 23.
According to the Fort Worth police department, Buchanan's blood alcohol level was twice the legal limit.
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Buchanan's letter of resignation was delivered on Tuesday and his equipment has been left at the police training center, his attorney told the Star-Telegram.
The department has not confirmed whether the resignation had been received.