Patrick, 30, a first-year psychiatry resident in Kalamazoo, was last seen on surveillance video at a hotel 5 minutes from her home. A hotel employee said she became agitated when he turned her away after offering to pay for a hotel room in cash.
Two hours later, her car was found in a ditch with a flat tire, 100 miles away from the hotel in Indiana. Her wallet was in the vehicle, but she and her car keys were missing, ABC News reported Thursday.
"We looked everywhere," said Sgt. Rick Strong of the Indiana State Police.
The YouTube videos show Patrick talking and singing to an unidentified person.
"Hi baby. I am just coming to you to say 'hi' and tell you about my day," she says in one video. In another, she is seen setting a table for two for a meal, and saying, "If you were here, this would be your plate."
The third video was shot at the hotel, CNN said.
Investigators say they have no evidence of foul play, but no suggestion Patrick's movements on Dec. 5 were voluntary, and hospital colleagues describe her as "part of our family of medical professionals," CNN said.
"It is the worst nightmare," her mother in Florida, Irene Patrick, said. "I really want this nightmare to be over."