Officers were called to a Motel 6 at 125 Silver Leaf Drive around 2 p.m. after housecleaning staff reported finding the girl's body.
Virgil was contacted and allegedly confessed to "acting alone to kill the child in a motel room at Motel 6," Thompson said.
"She was living in Aptos with her husband and she came down and rented the room and stayed at least one night," Thompson said. "She left the next day and left the child deceased in the room."
Thompson said Virgil's husband is the 3-year-old girl's stepfather.
While Virgil allegedly told police she acted alone, detectives have continued to investigate whether another person was present at the time of the girl's death, Thompson said.
The cause and time of the girl's death have not yet been determined, but the case is being investigated as an apparent homicide. Virgil has been booked into Santa Cruz County jail.
The murder is the city's third of the year, with two gang-related homicides reported in October, Thompson said.
Anyone with information about the case is asked to contact police at 831-768-3350 or the Crime Tip Line at 831-728-3544.