A letter from the Committee on the Scottish Government Handling of Harassment Complaints asks him to answer a series of questions and warned that without his submission the committee would be unable to quiz civil servants and ministers through the “perspective” of his evidence.
Committee chair Linda Fabiani also says in her letter that MSPs expect to take oral evidence from Mr Salmond in December and invites him to give his views on the evidence the committee has already heard.
The Scottish Government lost a judicial review of its handling of the complaints against Mr Salmond, and was forced to pay out £512,000 to the former first minister as a result.
The committee is now investigating how the allegations against Mr Salmond were investigated by the civil service and how the policy, which enabled the claims to be brought in the first place, was drawn up.
Ms Fabiani said the committee was contacting Mr Salmond again as it had not yet received any submission from him, despite first writing to him in July.
"Since July your legal representatives have set out the legal restrictions that prevent you from being in a position to provide a full account as requested by the committee,” she wrote.
“The committee has now explored the extent of the legal restrictions in relation to the judicial review including seeking the documentation held by the Court of Session.
"As a result I note the letter from Levy and McRae dated 13 October, which suggests documents from the judicial review that you are able to share will now be forthcoming in the near future.
"The committee requests, in addition to these documents, copies of relevant legal advice you received to inform your approach to the complaints handling process and the judicial review process.”
She adds: “Since the July letter was issued the committee has received numerous written submissions from others and has held evidence sessions on the development of the Scottish Government’s procedure for the handling of harassment complaints and has also held an initial exploratory session on the judicial review process.
"You should feel free to share your perspective on the evidence taken so far, including oral evidence on the development of the policy, and the judicial review and on the other written submissions received.
“The committee considers your evidence to be an important perspective in questioning Scottish Government officials and ministers in the final three phases of its inquiry.
"For that reason, I repeat again, on behalf of the committee the firm request to be provided with a written submission from you at your earliest opportunity, otherwise your perspective cannot be taken into account in questioning witnesses as the inquiry progresses.”
The committee has also written to former Permanent Secretary, Sir Peter Housden, pressing him for further information about harassment concerns he may have been aware of during his time in government.
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