A letter signed by 10 members of Strathclyde Police Authority calls on their chief executive to allow them to call in spending watchdogs and another force to investigate the allegations of misuse of public funds and misconduct.
The claims have been made by Sergeant Martin Porter, who is taking the authority to an employment tribunal, citing stress caused in part by how his reports and complaints have been handled.
The allegations include claims that, in June 2010, an operation was mounted to watch over the elderly aunt of ex-assistant chief constable John Neilson for no other reason than his personal friendship with the force's chief constable, Stephen House.
Mr Porter claims his complaint about Operation Park Road was not dealt with properly as the senior officer tasked with investigating was also the lead officer in the operation.
Although the police investigation found no evidence of misuse of public funds, Mr Porter has claimed relevant witnesses were not interviewed and when he raised this with former Deputy Chief Constable (DCC) Neil Richardson he was told he could bring his concerns to the Police Complaints Commissioner.
The signatories to the letter claim the allegations Mr House misused public cash should have been investigated by the authority's auditors and Audit Scotland should now be called in.
They discount the claim by the authority's chief executive, Keith Mannings, that the Operation Park Road allegations were not taken further by the body because Mr Porter did not co-operate, claiming the investigating officer himself should have been part of the probe. They also claim Mr Porter raised the matter directly with Mr Mannings.
Crucially, the signatories of the letter insist they "should have been informed by the DCC that a serious allegation had been made against the chief constable and given an opportunity to make a judgment about whether another force should be requested to investigate".
Although Mr Mannings was informed of the complaint it was not passed to authority members to bring in another force.
The letter adds: "We see no reason why the authority should not now have an opportunity to consider referring the complaint against the chief constable to the chief constable of another force, who should perhaps also be asked to investigate why the DCC did not bring the matter to the attention of the authority in November last year.
"The authority has a statutory duty to ensure complaints against police officers are carefully and impartially investigated in accordance with the regulations and the law."
The authority members also said allegations made by Mr Porter relating to his son's suicide and the investigation into an incident which preceded it should be referred to the Crown Office.
Authority member and Glasgow Liberal Democrat councillor Dr Chris Mason said: "The main duty of the police authority is to ensure the police are held to account in accordance with the law and regulations."
A Strathclyde Police spokesman said: "Strathclyde Police followed due process in dealing with a complaint against a chief officer. This complaint was initially investigated by Strathclyde Police Authority.
"The complaint was fully investigated and found to be unsubstantiated. The results of this complaint were made fully known to the officer and we have made him aware of the route of appeal open to him via the Police Complaints Commissioner for Scotland.
"The chief constable has always made it clear wherever a complaint is made it should be investigated properly and has no issue if the police authority ever chooses to refer a complaint to another force for investigation."
Last night, the police authority said: "In accordance with the usual procedure the chief executive asked for this complaint to be investigated by the force's Professional Standards Unit.
"In light of recent correspondence, members have asked for this to be considered by the authority and it will be considered at the earliest opportunity."