The uniformed officers were reported after a swastika was drawn on a napkin which was handed to one of the traffic officers. They now face a misconduct investigation.
Road traffic officers regularly visit police stations in Stirlingshire in the course of routine patrols in the Trossachs, an area popular with tourists.
It is understood the traffic police officers were known to frequent a takeaway and it was there that things came to a head with the swastika on the napkin last May.
Police Scotland confirmed they have launched an investigation and put two officers on “restricted duties”.
A source close to the investigation said: “There was regular banter between uniformed officers and traffic cops. The uniformed officers started calling them traffic Nazis’.
“They had been asked to stop but for some reason someone thought it appropriate to scrawl a swastika on a napkin at a takeaway where the traffic police get their breakfast. They were furious and complained to their bosses. Two uniformed officers have now been benched while an investigation is carried out.”
Police chiefs can put officers on restricted duties when a disciplinary process is ongoing. The sanction can mean an officer not doing a variety of routine duties, including dealing with the public.
One police source, who asked not to be named, said: “There may be occasions when you don’t want to suspend someone because you want to get some work out of them so by putting restrictions on them you can say to them they are doing parking tickets in a back office.”
MSP Dean Lockhart, who represents the mid-Scotland region in the Scottish Parliament, said: “The vast majority of officers across the Stirling area, and throughout Scotland, act with the professionalism the public expect.
“If the internal investigation was to conclude that the officers involved in this incident did act in a way which breaches these high standards then I would expect Police Scotland to take the necessary disciplinary action.
“There is no place for hate speech or discrimination of any kind in Scotland, and any instances should be treated with the seriousness they deserve.”