Lawyers for Bishop and The Boston Globe are to make arguments before the Supreme Judicial Court on Tuesday.
The Globe says the report should be made public because there is interest in finding out what went wrong with the original investigation into Seth Bishop's death.
Police in Braintree, Mass., ruled it accidental.
After Bishop was charged with killing three of her colleagues at the University of Alabama last year, Massachusetts authorities re-opened the investigation.
An inquest led to her being indicted for murder in her brother's killing.
Bishop's lawyer says releasing the inquest report could prejudice juries against her in both Massachusetts and in Alabama.
(Copyright 2011 by The Associated Press. All Rights Reserved.)