SNP MSP Michelle Thomson raised concerns this could put some complainers off.
New rules will see complaints about current and former ministers handled by external and independent investigators following the unlawful investigation into claims of sexual harassment by Alex Salmond.
The botched investigation into the former first minister was ruled to be unlawful by the Court of Session, prompting three inquiries into the Government’s handling of the affair and its complaints procedure.
Where a crime may have been committed, the new procedure says the Government "will, wherever possible, respect the wishes of the complainer".
However, it adds there may be circumstances where the Government has "an obligation to bring the matter directly to the attention of the police".
During its handling of the Salmond case, the Scottish Government reported allegations to the police despite the reluctance of complainers.
Speaking at Holyrood's finance and public administration committee on Tuesday, Ms Thomson asked: "What active consideration have you given that that could actually have a cooling effect on complainants – completely the opposite intention?"
Mr Swinney said it was a "very difficult question", but argued there had to be “an acceptance of the particular obligations that apply to Government”.
He said this would be considered on a "case-by-case basis".
Earlier, Mr Swinney told the committee: "As an employer, the Scottish Government is not under an absolute duty in all circumstances to report matters that it believes may be a crime to the police. It's not under a statutory duty, as an employer.
"But I would consider that the Scottish Government, for the purposes of ethics, if it considered it had knowledge of a crime having potentially been committed, would have to give very serious consideration to referring that to the police, even if an individual who was a member of staff who was perhaps a victim of that alleged crime did not want that to be the case.”
Responding to Ms Thomson, Mr Swinney said the Government would consider whether it has “got the balance of that thinking correct”.