Rosebud is a city in Falls County, Texas. The population was 1,493 at the 2000 census. As of July, 2007, the population was 1,348, an -8.4% change since 2000. Rosebud is the birthplace of NFL running back LaDainian Tomlinson. It is also the birthplace of Kenneth McDuff, a serial killer suspected of at least 14 murders.