Father of Jamie Lynn Spears' baby injured in car crash

Casey Aldridge Jamie Lynn Spears Maddie

, sustained a head injury in a car accident early Sunday morning.

Sources say that Spears, 18, and Aldridge's sister are at his side at the University of Mississippi Medical Center, though hospital staff there would not confirm that Aldridge is being treated there.

A family source tells People that Aldridge has "a cracked skull" and has been "in and out" of consciousness, but that the injury is "not as serious as we thought at first."

Aldridge, 19, was driving his truck with several passengers inside when it went off the shoulder of the road and flipped over, sources say.

Police have not commented on the accident. A rep for Spears has yet to comment.