North Yorkshire Police said detectives investigating the death of Lydia Bishop at the nursery at York College last month have spoken to the members of staff who have been released on bail.
Lydia suffered serious injuries in an outdoor play area on September 17. It was her first day at the nursery.
A police spokesman said: “Detectives investigating the death of Lydia Bishop, aged three, at York College Day Nursery have interviewed two members of staff.
“The staff members were interviewed as part of the ongoing inquiries into the circumstances surrounding Lydia’s death.
“The investigation is still in its early stages and it is not possible to comment further at this time.”
Emergency services were called to the nursery on the afternoon of September 17 and Lydia, from York, was taken to York District Hospital, where she was pronounced dead.
A joint investigation with the Health and Safety Executive has been launched into the incident, which police said they were not treating as suspicious.
Her death was described by the college as “absolutely devastating”.
An inquest into Lydia’s death was opened and adjourned earlier this week.
The coroner was told that Lydia was found unresponsive on a slide with a piece of rope around her neck.
He was also told that staff and paramedics battled to save her life.
The nursery opened in 2007 and provides full daycare for children aged between six weeks and five years.