Police are "looking at" Wakefield City Academies Trust (WCAT), Tes can reveal.
In September, the multi-academy trust announced it was giving up all its 21 schools after concluding it was unable to rapidly improve them.
The trust's schools are set to be re-brokered to eight other academy chains. However, the collapse of WCAT has generated additional controversy because a number of its schools claim they had money transferred to the trust's central accounts which now will not be returned.
Last month Wakefield Council passed a motion calling on the government to ensure "full restitution of all money transferred from schools reserves into WCAT’s central accounts" and demanding "that WCAT is not dissolved until its affairs have been fully investigated and the results made public".
During the meeting, councillor Peter Box, the Labour leader of Wakefield Council, said he would be referring the matter to the police. "There are serious questions to be answered about the way that money has been dealt with and it would appear has not been given back," he said.
He added: "I'm surprised that the government has not referred it to the police, but we will do what the government won't do and make sure there's a full investigation into financial affairs that have been going on."
In a statement, a spokesman for West Yorkshire Police told Tes: "Following further discussions with the local council, information has been now passed to us which we are looking at.
"No crimes have been recorded at this stage and consultations are ongoing with relevant authorities."
'Move forward and improve'
Minister Nick Gibb has said that WCAT "will not be able to retain any of the reserves that it holds at the point of dissolution”.
The Department for Education has also said it is "working with WCAT to transfer its schools to new sponsors ensuring each one has a secure financial basis, as well as the necessary funding to move forward and improve”.
WCAT was contacted for comment.