A complaint has been made against the chief constable over an alleged conversation with an MEP.
It is claimed that Gillian Parker spoke to Euro-MP Tom Wise and told him that no action would be taken against him in relation to allegations of fraud.
The police are investigaiting as they are obliged to do with any complaint they receive.
The complainant, who has asked for anonymity, levelled claims of fraud against Mr Wise over a year ago.
Accusations of expenses fraud by Mr Wise totalling some £45,000 are now being investigated by Bedfordshire Police after a referral from EU antifraud body Olaf.
The force has questioned people close to the UKIP MEP, who is based in Leighton Buzzard High Street.
Former policeman Mr Wise established his offices in Bedfordshire when he was elected as a UKIP Member of the European Parliament in 2004.
In autumn last year the original complainant became frustrated by what he regarded as 'stalling' by the police.
He wrote repeatedly to the force complaining that he had not been given a crime reference number.
He then learned that Mr Wise had allegedly written an email to a fellow MEP claiming that Mrs Parker had assured Mr Wise he would not be investigated.
The complainant passed the MEP's contact details to Bedfordshire Police in January this year and the complaint against Mrs Parker was assigned reference number Co/00281/07.
Police Authority chairman Peter Conniff said: "I am aware that a complaint has been made against the chief constable.
"Following normal procedure this is being investigated by the Police Authority and at this time I can make no further comment."