It happened just west of the State Capitol building around 3:45 a.m.
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The trooper was patrolling the area of Colorado Street and was making a turn onto West 13th Street when they ran over the person who was lying in the street, according to DPS officials.
The victim, a 50-year-old man, died at the scene, according to Austin Travis County EMS.
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The Texas DPS Capitol Region was investigating, KXAN reported.