The prosecution is appealing a judge's decision last month to dismiss two murder counts against Costa.
Angel Jorge Posca, 58, of Palmdale and his 12-year-old daughter Angelina died after the truck Costa was driving slammed into their car while coming down Angeles Crest Highway in April. Several other cars were also struck in the process.
Costa's attorney says the appeal will not succeed because the deaths do not qualify as murders.
For now, he is charged with vehicular manslaughter.