An inquiry is being urged after claims in a newspaper that the chief constable of Cambridgeshire made inappropriate sexual comments to a woman official.
In a statement, Mr Lloyd was said to be sorry for any offence caused
Tom Lloyd, 53, has apologised for any offence he caused during the Association of Chief Police Officers' (Acpo) annual conference in Birmingham.
According to the Daily Mail, the woman was allegedly "pestered", although she reportedly made no official complaint.
A Police Federation spokesman said the Police Authority should investigate.
In a statement, a Cambridgeshire Police spokesman said: "The article refers to a private evening event where people were winding down and having after-dinner drinks.
"There were no issues between Tom Lloyd and the unnamed official.
"However, it is clear that some people appear to have been concerned and Mr Lloyd is very sorry if anyone was offended in any way."
Cambridgeshire Police Federation chairman Mike McFadyzean said: "It is clear that Tom Lloyd has apologised for some aspects of his conduct that particular evening. It is also clear that other senior officers were present.
'Too much drink'
"In view of that I believe it is incumbent upon the Police Authority to initiate an inquiry into this matter.
He said they needed to find out if Mr Lloyd's "conduct significantly impacts upon his credibility and ability to be the chief constable of Cambridgeshire".
A Cambridgeshire Police spokesman said the Police Authority had not yet decided if any action would be taken.
Chris Fox, president of Acpo, said during the conference he had been told that a member had "apparently had too much to drink" and his "behaviour was causing concern to others".
He said he spoke to those concerned at the time of the incident and the following day and on both occasions was "reassured that the matter was closed".
Mr Lloyd was appointed chief constable shortly before schoolgirls Holly Wells and Jessica Chapman went missing from Soham in August 2002.
He faced criticism when it emerged that he had gone on a family holiday during the hunt for the missing schoolgirls, while many of his officers were putting in 20-hour days.
He cut the trip short and returned home.
Mr Lloyd was later called as a witness in the Bichard Inquiry into how police cleared the girls' killer, Ian Huntley, to work at a college despite a string of sex allegations.
Mr Lloyd told the inquiry that he took full responsibility for errors made and failings in vetting processes.