F.'s parents told police they had "no indicators" of "any type of relationship between these two," Murray Smith, public information officer for the Columbia County Sheriff’s Office, told ABC News today.
From interviews, authorities said they have learned of what Smith described as the "blossoming of a potential relationship" between F. and Rodriguez.
"C. has a current boyfriend who also is beside himself because everything was fine," Smith said.
He said F. has family in New York and Rodriguez has family in Canada and possibly Pennsylvania.
Authorities are urging people along the I-95 corridor to keep a lookout, Smith said.
As of today, this isn't considered a kidnapping case as no criminal charges have been filed, Smith said.
But Smith added: "For her to be on the road with this gentleman, I consider that to be a dangerous situation."
"We are hoping for a great resolution," Smith said. "We don’t want them to think they are in trouble. They’ve made some poor decisions but who hasn’t? Just want them to contact their families and come home."
The FBI is assisting the sheriff's office with the case.