The Boston police continued their investigation this week into the murder of Joseph Strickland, the late assistant to the dean of the Graduate School of Arts and Sciences.

John W. Maillet, the police sergeant conducting the investigation, has apparently narrowed his list of suspects down to "one female acquaintance" of Strickland's, but he does not have enough evidence to make an arrest.

There was another death in the Harvard community this week. Eleanor T. Glueck, a retired research associate in Criminology at the Law School, was found dead in her home Monday.

According to Maillet, Strickland returned home last Friday morning at about 1 a.m. He immediately placed a long distance telephone call to a friend. While he was talking on the phone, the suspect let herself into the apartment. She began speaking to Strickland in a voice loud enough that the person on long distance could hear her voice Maillet believes that sometimes between 1:30 a.m. and 7:30 a.m. she shot Strickland.

By contacting people listed in an address book found in Strickland's bedroom, Maillet determined the suspect's identity. Much of the information Maillet got from those listed in the book was off the record and almost all of them told him they would not testify in court.

Because of the lack of evidence. Maillet is uncertain when he will be able to make an arrest. To keep track of the suspect, however. Maillet's informants are watching her to make certain she does not try to leave the Boston area.

Until an arrest is made, the police will probably be reluctant to give out more information. After Maillet revealed on Tuesday that the main suspect in the case was a "female acquaintance" of Strickland's. Lieutenant Edward Sherry, the head of Boston's homicide division, put a blanket on further news coverage of the investigation.