At the disciplinary hearing before Chief Constable Sir John Evans this week, the officers, an inspector, a sergeant and a constable, admitted neglect of duty. Two other sergeants will be admonished and two constables and a member of the support staff will be informally disciplined.
Ms Rappai, 33, a former computer engineer, went missing from her father's home in Rugby on March 13 1998.
She was found in Devon then moved into Cornwall where she lived in her car for six months, before being found dead at the Gorran Haven car park near St Austell on August 27 1998.
An inquest decided she died from natural causes due to malnutrition and mental illness.
Her family complained about the way the police had dealt with the case and an investigation was carried out by the independent Police Complaints Authority.
The inquiry found officers in Okehampton and Helston had considered using powers under the Mental Health Act to detain Ms Rappai, but considered they would be abusing them. Helston officers were making considerable efforts to ensure she was being cared for and the investigation agreed they would not have had lawful justification at that time to detain her.
However, the investigation found there had been a failure between the three forces to co-ordinate information about her and the car she was driving and a failure to co-ordinate internally and within individual forces.
The investigation found there was no policy or procedure in place for those people not coming within the definitions of the Mental Health Act, but still requiring help.
Officers did not consider referral to Social Services or voluntary mental health organisations, both possible options, because they were not trained to do so.
These deficiencies have been addressed by the constabulary, which has also employed the services of a qualified psychiatric nurse.
A review of all command and control procedures has also taken place, so too a review of how computer checks of people and vehicles are made.
The training of force enquiry operators and the grading of emergency calls has also been reviewed.
Following the hearing, the chief constable expressed his sympathy to the family and said he regretted the force had, on this occasion, fallen short of its high standards.
He said Ms Rappai was a bright, intelligent woman who had chosen a particular lifestyle.
He said she clearly did not want the police involved, and though officers had tried to help, they were in a difficult situation and their actions were restricted.
'We will ensure we learn lessons from this tragedy,' he said.