Assumed Name of Gerhard

According to testimony given to Brazilian police by the Bosserts, they met Dr. Mengele through an Austrian friend, Wolfgang Gerhard, who returned to Austria in 1975 and left his Brazilian identity card with Dr. Mengele.

Mrs. Bossert said Dr. Mengele put his own photograph on the card and assumed the name of Mr. Gerhard, who she said died in 1977. She added that she rented a house to Dr. Mengele, ''who would receive money for his sustenance sent by his family in Germany''.

In the police record of her testimony, she said Dr. Mengele ''was always apprehensive and feared being discovered by the Jews.'' In his separate testimony, Mr. Bossert said Dr. Mengele ''avoided talking about the Second World War and lived apprehensive and afraid, fearful of being found by Jews''.

The couple told the police that Dr. Mengele would visit their home in the Sao Paulo neighborhood of Brooklin at least once a week because ''he was very lonely and needed people to talk to'' and that together they would listen to German and classical music. Their children knew him by the nickname of Titio, the Bosserts said; Dr. Mengele had previously used the name Pedro.

Drowned at Beach Resort

They said that in February 1979 Dr. Mengele accompanied them to the beach resort of Bertioga, 65 miles east of here. They said that on Feb. 7, 1979, he suffered a stroke while swimming and drowned. Mr. Bossert said he tried to save him and almost drowned in the process.

According to both their testimonies, Dr. Mengele's body was then taken to Embu, where he was buried under Mr. Gerhard's name in a tomb where Mr. Gerhard's mother, Friederike, had been buried after her death in 1961.

They also said that the administrators of the cemetery had known the real Mr. Gerhard and had wanted to open the coffin but that Mrs. Bossert had become hysterical at the suggestion and that the box had remained unopened until today.