But they say Caoimhe McEvoy has been unable, so far, to provide any clues as to what happened to her during her 20-hour ordeal.
She was found wandering along a roadside 20 miles from the hotel in Orlando where she and her family were staying.
Commander Steve Jones, from the Orange County Sheriff's Office, said that although she was physically unhurt, she was shy of the officers who tried to interview her, and was unable to pass on any useful information.
"We've not got too many leads," he said.
"Investigators tried talking to her but she's very quiet. According to her parents, that's her nature. I think they're going to let her settle down.
"She's fine physically. The examination by doctors didn't show any injury on the outside - cuts or bruises or anything.
"They're waiting for results on internal tests but she seems normal."
Attempts to question her were expected to resume later yesterday using specially trained officers from the local child protection team.
Mr Jones said Caoimhe had been discharged from the hospital where she was taken for checks and was now recovering with her parents at another hotel.
The family had been due to fly home on Monday at the end of their two- week holiday.Reuse content