Witnesses say 45-year-old Larry Dale Duke drove through a stop sign in Ceres on Wednesday morning and hit the students as they walked to their junior high school.
Thirteen-year-old Danielle Tarancon-Leon, a seventh-grader at Mae Hensley Junior High School, died at the scene.
Eighth-grader Nancy Zavala remained in critical but stable condition Thursday after knee surgery, police said.
Public records show that Duke has a record of traffic violations that include speeding, driving under the influence, driving without insurance and driving with a suspended or revoked license, the Modesto Bee reported.
Duke has not been arrested in the case. Ceres Police Chief Art de Werk says possible charges could range from vehicular manslaughter to some form of homicide.
The department will likely send its recommendation for charges to Stanislaus County prosecutors by the end of next week, police said.
Duke has been hospitalized in Modesto for undisclosed medical issues since Wednesday's accident, according to Sgt. Dan Vierra, who's leading the investigation.
Duke apologized in an interview with KXTL-TV hours in his hospital room after the crash.
"I'm so sorry this happened," he said. "I know it's harder for you guys to sit there and accept anything I'm saying, but I am so sorry it happened. I didn't mean for it to happen."
Information from: The Modesto Bee, http://www.modbee.com