The Welsh Government has clarified its advice to staff giving evidence to the Carl Sargeant inquiry after an email emerged asking them to tell civil servants if they had any.
Paul Bowen QC is investigating Carwyn Jones's handling of the sacking of the Alyn and Deeside AM from his cabinet.
Opposition groups said the email raised doubts about the probe's independence.
The Welsh Government said advice had been updated to make it clearer staff could contact the inquiry directly.
Mr Sargeant was found dead in November, four days after being dismissed.
The Alyn and Deeside AM had been facing a Labour Party inquiry into allegations of "unwanted attention, inappropriate touching or groping" towards women when he died.
In an email to Welsh Government staff entitled "support to staff", the permanent secretary asks "those who believe they have evidence relevant to the investigation should bring this to the attention of David Richards, Director of Governance; Peter Kennedy, HR Director; or my office".
Dame Shan's email also lists support options for staff affected by the death of Carl Sargeant.
Welsh Conservative leader Andrew RT Davies said the email "once again raises serious concerns over the conduct of the Welsh Government and calls into question the independence of this whole process".
"If the inquiry is to be fully independent then all potential evidence should be handed over to the QC leading the investigation, not pre-vetted by the permanent secretary or her minions," he said.
"The Welsh Government must apologise and immediately withdraw this instruction so people can provide evidence to the inquiry free from bully-boy tactics and intimidation."
Plaid Cymru said it would be raising the matter with Welsh ministers urgently.
A party spokeswoman said: "This raises serious questions about the internal processes of the Welsh Government and risks jeopardising the independence of the inquiry.
"It is vital that this inquiry remains independent, transparent and fair."
A spokesman for the permanent secretary said: "We have been clear that as a civil service we will fully co-operate with the work of the IQCI [independent QC investigation], and any evidence held by staff on Welsh Government systems will be collated and transferred to the investigation in its entirety and without redaction."
The spokesman later added: "We have also updated our intranet [private website] to make it clearer that staff can contact the IQCI directly if they wish."
A spokeswoman for the inquiry said: "Mr Bowen QC would like to receive evidence from all potential witnesses.
"Any potential witness who would like to give evidence to the investigation directly may contact the solicitor to the inquiry in the first instance ... all approaches to the investigation will be kept confidential, if requested."