A Police Scotland detective chief superintendent said they and the chief constable, Iain Livingstone, "both voiced our concerns" about the Government's plan to announce there were allegations of sexual harassment by the former first minster before police had investigated the claims.
The extract of the witness statement was released after the Holyrood inquiry into the Government's unlawful investigation of Mr Salmond used powers in the Scotland Act to demand the Crown Office release evidence.
It also confirmed that Crown Agent David Harvie offered to give the police a copy of the findings of the Government's internal investigation - an offer that was rejected.
In the witness statement, the detective chief superintendent - whose name has been redacted - recounts the meeting where police were told that the government had referred the complaints about Mr Salmond to the Crown Office "for investigation of potential criminality".
They said that it was agreed a "proactive approach" was required to identify other potential complainers, including by contacting other people who held similar roles to the women who had already come forward.
They added: "Mr Harvie was in possession of a copy of the Scottish Government s internal conduct conclusion report and offered to provide me with a copy. I refused this offer and neither I, nor the chief constable, viewed this document.
"I was also informed that Scottish Government may be making a public statement in relation to the outcome of their investigation and potentially refer to information being provided to Police Scotland.
"Both the chief constable and I both voiced our concerns about such a statement being provided.
"As such, it was agreed that the main priority was to make contact with the two individuals who had made a complaint to the Scottish Government."
The former SNP leader subsequently challenged the lawfulness of the investigation and the Government eventually conceded the judicial review after prior contact between the investigating officer fatally undermined their defence.
Lord Pentland at the Court of Session described the investigation as "unlawful" and "tainted by apparent bias", and Mr Salmond was awarded the maximum possible legal costs of £512,250.
He was later acquitted of 13 charges of sexual assault at Edinburgh's High Court.
Responding to the Holyrood committee's Section 23 order for the release of the operational witness statement, Procurator Fiscal Kenny Donnelly also offered to share its notes from the evidence given under oath by the detective chief superintendent during the criminal trial.
When giving evidence to the committee, Ms Salmond said he was told the government planned to issue a public statement announcing it had investigated two women's complaints and was passing it on to the Crown Office.
Mr Salmond said he thought that would be "remarkable" because "any hope of confidentiality in the process would have gone once that statement had been made".
He then said the government's plan was "even more remarkable" once he learned that the Crown Agent "was advised against any publicity by the police in a meeting two days previously".
Around the time that the government had intended to make a statement, details of the investigation were leaked to the Daily Record, who then broke the story.