Wilkinson said there were no obvious signs of trauma or foul play, but said investigators will consider her death suspicious.
"There are certainly possibilities of suicide. There are certainly possibilities of an accident. And we certainly can't rule out homicide," he said.
Wilkinson said the woman's body will be taken to Baltimore for an autopsy.
"That's going to tell us a lot, a tremendous amount," he said.
Among other things, investigators hope to learn whether the woman drowned and how long she had been dead, Wilkinson said.
Authorities received several phone calls on Monday about a vehicle in the Potomac River near River Bottom Park in Williamsport. Wilkinson said the car was in 5 feet of water about 50 to 60 feet offshore when authorities arrived shortly after 4 p.m.
Investigators tried to piece together the circumstances leading to Monday's discovery. Wilkinson said the woman was known to frequent the Williamsport area.
Fire and rescue companies were sent to River Bottom Park at about 12:20 a.m. Saturday for a report of an accident after someone called 911 from a pay phone.
"At that time, we found nothing," said Will Ball, chief of the Williamsport Volunteer Fire Co.
Ball said officials searched but could not find evidence of an accident or the caller. While fire and rescue units sometimes are sent to accident scenes where nothing can be found, Ball estimated it happens less than 3 percent of the time.
"Most of the time, it's during a storm when a car slides off the roadway," he said.
Bill Grimm, assistant chief of the Williamsport Volunteer Ambulance Service, said rescue units located the car in the water on Monday and called two divers who searched the area and discovered the body.