Knox County Sheriff David Barber said Sarah Maynard's mother, Tina Herrmann, is still missing, along with her 10-year-old brother, Kody, and her mother's 41-year-old friend Stephanie Sprang.
Barber said 30-year-old Matthew Hoffman was arrested on one count of kidnapping at his home in Mount Vernon, about 40 miles north of Columbus, and that more charges are expected. He said reports from neighbors that a body bag had been taken from the home are false.
"We have no one that we're aware of who is deceased," Barber said. "So we're still treating this as a missing person's case."
He did not know if Hoffman was connected to either Herrmann or Sprang, but said he is not the ex-boyfriend of either woman.
Barber said authorities hoped Hoffman would give them information leading to the other three.
"We were hopeful of finding more than one of the missing people in the house," he said. "But the information we had was that Sarah would definitely be found in that house."
Barber said the girl was hospitalized in good condition. He did not say what led them to the home.
Authorities believe the girl had been "under the control" of Hoffman since Wednesday, when she and her brother last attended school, Barber said. Their mother was reported missing that day when she did not show up for work at a local Dairy Queen.
Barber has said blood indicating an injury had been found in Herrmann's home, where the friend's vehicle was in the driveway.
Herrmann's pickup truck had been found Thursday night near the Kenyon College campus, leading to a lockdown at the school.