The Police and Crime Commissioner (PCC) said she had received a complaint relating to Andy Marsh's role in Hampshire Constabulary's investigations at Stanbridge Earls School in Romsey.
A 2014 inquiry by Essex Police cleared him of misconduct allegations.
Another force is now set to investigate the complaint.
During Mr Marsh's tenure as Hampshire chief constable, the force investigated two rape claims against students by a girl at the independent school for pupils with special needs in 2013.
Following allegations of misconduct against Mr Marsh over his handling of the investigation, a report by Essex Police found "no grounds to justify" the claims.
Avon and Somerset PCC Sue Mountstevens said she had received a complaint relating to meetings held by Hampshire Constabulary during its investigation into the rape claims.
"I reviewed this latest complaint and given the background and the previous 12-month investigation I felt the complaint could be dealt with locally and directly with the complainant," Ms Mountstevens said.
"The complainant has the right to appeal my decision.
"They have used that right, and the Independent Police Complaints Commission has referred the complaint back to me for local investigation, which means I will ask another police force to look at this."
Following the police investigation and Ofsted inspections which raised concerns about safeguarding of pupils, the independent school, which had boarding and day pupils aged from 10 to 19, closed in 2014 after calling in administrators.
Mr Marsh replaced Avon and Somerset chief constable Nick Gargan, who quit after being found guilty of misconduct by an independent panel.
Avon and Somerset Police's chief constable is to be investigated over how his previous force dealt with abuse claims at a special needs school.