Various reasons have been given by senior officers, but the force is being told it needs to be “open and transparent” if it wants the help of the public.

Monifieth councillor Frank Ellis said, “When I read the story yesterday I became more concerned that there had been an incident that hadn’t been revealed. If the police are looking for help and assistance from the public to find this lady, it is very important to be open and transparent.”

Mrs Hill was given a fixed penalty after spending time in the cells for a breach of the peace while out with her husband Kenny on the evening of April 5.

The fact she was dropped off by officers at Riverview Caravan Park less than an hour before her reported disappearance was not made public by police until sources tipped off the Tele.

The man then leading the inquiry also allowed her husband Kenny to tell a Press conference that the lead-up to her disappearance had been a “normal” night out without ever challenging that assertion.

Defending their position, a spokesperson said, “What constitutes a normal night out for Mr and Mrs Hill might not be a normal night out for you or I.”

The spokeswoman said Mr Hill (44) was entitled to say “whatever he likes” and that he was not “scripted or gagged” by Tayside Police.

“We have always been aware of the full circumstances surrounding Linda’s disappearance and, as with all police investigations of this kind, information is often held back for valid operational reasons pertinent to the inquiry,” she continued.

The force has also said that identifying an individual who had received a fixed penalty would be a breach of data protection law, and that Mrs Hill was entitled to privacy.

Mrs Hill (41) was last seen on Sunday, April 6, when she went for what was described as an “out of character” walk from her home at the busy waterfront caravan site.

She had been out the previous night in Broughty Ferry and Monifieth as she recovered from pneumonia. Previous accounts of the night have led the public to believe the couple had returned home as normal.

However, it has since emerged she fell in front of a car in Reform Street. Police officers were alerted to the incident and the mother-of-one was taken into custody.

There have also been reports Mrs Hill had moved out of the caravan prior to her disappearance, but the spokeswoman would only say, “Individuals are entitled to a private and personal life. If the Senior Investigating Officer felt releasing specific information about her private life would assist the inquiry, he would have done so.”

Despite repeated appeals for information, it appears police have no new leads since a member of the public reported seeing someone in the water at Monifieth around the time Mrs Hill disappeared.

Councillor Ellis said he believed the people of Monifieth would always help the police “with the best interests” of Mrs Hill in mind, despite being kept in the dark about the arrest.

He added, “It’s unfortunate and I hope it’s not the reason for her going missing.”

Mrs Hill was believed to have been wearing a blue two-tone Regatta jacket, a white shirt, dark jeans and black knee-length boots. She is around 5ft 2in, of medium build with brown hair and brown eyes and has a dolphin tattoo on her shoulder.

Major searches have been carried out, and family and friends have been interviewed. A forensics team also examined the couple’s caravan.

Police board convener Councillor Ian Mackintosh is to request a meeting with Detective Chief Inspector Caughey to discuss their handling of the situation.

Mr Mackintosh said today he had not been fully aware of all the facts and could only respond to the information supplied to him by the Tele.

He said today, “The main focus for the police is to find Mrs Hill. There are issues of data protection in some cases and it is up to the senior officer whether or not to give that information out. Until I am in full possession of all the facts I wish to make no further comment.”