The allegations faced by Phil Gormley are serious, and both the Liberal Democrats leader Willie Rennie and former Association of Police Superintendents president Niven Rennie have urged him to step aside.
There is also a precedent of senior officers - albeit not as high in the ranks - being put on restricted duties while under investigation.
However, at present, we are at the stage of a complaint being made, rather than evidence of wrong-doing being presented. On that basis, Mr Gormley should not have to step down pending the results of the investigation.
If a senior figure such as the chief constable had to stand down automatically every time a complaint was lodged, the process would be open to abuse.
It should also be kept in mind that few police officers will get through their career without having a complaint lodged against them, whether internal or external.
In the police force, it more or less comes with the territory.
The Scottish Police Authority, which holds the national force and its chief constable to account, has wisely left the door open to changing circumstances.
In its statement, it said the appropriateness, or otherwise, of suspension “is an issue we will keep under review”.
However, the decision to allow Mr Gormley to continue in his post requires the Police Investigations and Review Commissioner (Pirc) to conduct a transparent and swift investigation into the allegations.
Police Scotland has been dogged by a series of controversies since it was established four years ago, many of them involving its previous chief constable, Sir Stephen House.
Laying aside the rights and wrongs of the rows over issues such as stop and search and armed police, the reputation of the force was dented.
It has struggled further over the failure to properly log a call which led to a couple who died after a crash on the M9 being left in their car for three days.
The Gormley case must be cleared up, satisfactorily and without delay, so any uncertainty hanging over the leadership of Police Scotland does not drag on.
Pirc investigations often take a considerable time, but this one is urgent.