Labour has raised concerns over the validity of traffic tickets and other police documents issued while the country has no formal chief constable.
Sir Stephen House formally left office at midnight on December 1 - but his replacement, Phil Gormley, is not due to take up his post until the same hour on January 4.
The national force is currently being run by Deputy Chief Constable Neil Richardson, an unsuccessful candidate to replace Sir Stephen.
But Mr Richardson has not been given a temporary promotion to chief constable - meaning he holds the office as a "designated" deputy.
Officials at the Scottish Police Authority believe this, under current legislation, is more than enough to ensure the robustness of all notifications, such as fixed-penalty notices or fines, issued in the name of chief constable.
Labour's Graeme Pearson, himself a former police chief, questions this.
Mr Pearson said: "The police are putting these notifications in the name of Sir Stephen House when Sir Stephen House no longer exists. He has gone.
"How can the deputy operate legally on behalf of somebody who no longer exists in the service? There is some difficulty there.
"Given the number of notifications of offences are being issued in this interim period, it is unhelpful that there should exist this confusion about the legality of the process and the sooner it is cleared up the better for all concerned."
Mr Pearson said he was raising concerns on behalf of a member of the public and that he would be in touch with Police Scotland on the issue.
The Herald understands that Mr Richardson did seek an interim appointment as chief constable. Insiders have confirmed there was an exchange of correspondence on the issue as power was handed over.
A spokesman for the SPA said: "We have delegated Neil Richardson as the deputy chief constable to carry out the chief constable's functions until Phil Gormley takes up his post on 5 January.
"Under that designation, Mr Richardson has the same range of powers as a permanent Chief Constable in the exercise of his duties.
"This includes, but is not restricted to, all police operational matters, budgets, signing authorisations and warrants, and police officer and staffing matters."
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