Only one person was dismissed from the jury pool on Wednesday. The woman indicated she had some previous contact with Spears' business manager.
Questioning was scheduled to restart on Thursday morning, and opening statements could begin later in the day if a jury is seated.
The charge is the last remnant of a case that stemmed from an accident last August in which Spears, who did not have a valid California license, hit a parked car and left the scene. Drivers are supposed to get a California license within 10 days of establishing residency.
Spears, 26, did not appear in court on Wednesday, and may not attend the trial. Her attorney said Wednesday that no final decision on Spears' participation in the trial had been made.
Her father, James Spears, may be called as a witness in the case, which is expected to last three days. Other potential witnesses include police officers and an online producer for gossip site X17online.com.