Court staff said on Friday that they had received an application for permission to appeal against all of the nurse’s convictions.
Letby, 33, was sentenced to a whole life order after jurors convicted her of the murders of seven babies and the attempted murders of six others at the Countess of Chester Hospital’s neonatal unit in 2015 and 2016.
The Department of Health has previously said that an independent inquiry will be held into Letby’s case, and will examine “the circumstances surrounding the deaths and incidents – including how concerns raised by clinicians were dealt with”.
Typically, applications for permission to appeal against a crown court decision are considered by a judge without a hearing.
If this is refused, people have the right to renew their bid for permission at a full court hearing before two or three judges.
The hospital saw a significant rise in the number of babies suffering serious and unexpected collapses in 2015 and 2016.
Letby’s presence when collapses took place was first mentioned to senior management by the unit’s head consultant in late June 2015.
Concerns among some consultants about the defendant increased and were voiced to hospital bosses when more unexplained and unusual collapses followed, her trial at Manchester Crown Court heard.
But Letby was not removed from the unit until after the deaths of two triplet boys and the collapse of another baby boy on three successive days in June 2016.
She was confined to clerical work but registered a grievance procedure, which was resolved in her favour, and was due to return to the unit in March 2017.
The move did not take place as soon after police were contacted by the hospital trust.