The justices on Monday turned down a request by the Roman Catholic diocese in Bridgeport.
It's unclear when the documents will be released. The judge in the case scheduled a Nov. 9 hearing and asked attorneys from both sides to submit written arguments about how the documents should be made public.
Several newspapers are seeking the release of more than 12,000 pages from 23 lawsuits against six priests.
Diocese officials said the content from those pages has been reported on extensively and said the Supreme Court decision threatens churches’ First Amendment rights and privacy rights for litigants.
The records have been under seal since the diocese settled the cases in 2001. Courts in Connecticut have ruled that the papers should be made public.
"For more than a decade, the Catholic Church in Bridgeport has addressed the issue of clergy sexual abuse compassionately and comprehensively,” diocese officials said in a statement released Monday. "For now, however, the serious threat to the First Amendment rights of all churches and the rightful privacy of all litigants remain in jeopardy because of the decision of the Connecticut Supreme Court. This, indeed, is regrettable."
In August, Justice Ruth Bader Ginsburg dealt the church a major blow by ruling that the documents could not remain sealed as the nation's high court decided whether it would review the case.
In September, Justice Antonin Scalia passed the request to the full court, who ruled on it on accepted the request.
Critics have said the move was an attempt to protect former Bishop Edward M. Egan, who moved many pedophile priests around the diocese even after learning about sex abuse allegations, according to the Hartford Courant.
Nearly two-dozen lawsuits against seven priests in the diocese were settled for an undisclosed amount of money in 2001.
Four newspapers, including the Courant, went to court in 2002 seeking to have the files reopened and to keep them from being destroyed. The Connecticut Supreme Court has ruled twice that the files are public.