I can't necessarily speak to the public release of Family Court records, governed under the Civil Rules of Procedure, because by the very nature of civil matters, there are Statutory reasons long in place for why certain records are not accessible to the public. Nonetheless, I think we agree that Shoenhorn is most likely behind MT's barrage of Tweets with attachments, and not likely he's used her cover to disclose anything not covered by the first amendment. That doesn't mean we have to like it!
However, what you are saying about publicly accessible Civil records being available for viewing in person at the courthouse, court kiosk, etc., seems to me to be universal. I know printing the document is available at some Court desks for a king's ransom of $1-2 per page! But to be clear, under both Civil and Criminal procedures, there's a difference between a record being sealed by Court Order (disclosed by the court clerk to defense counsel, defendant, or prosecutor for limited purpose), and a record made inaccessible to the public.
In the matter of the third party, Family Investigation Report that was Ordered prepared by the Court, the Court sealed this record when the hearing on the matter involving the report was incomplete because the party left the hearing before the hearing was concluded. As to ever making this report public, I think the Court has been clear that this is not an option. (Also see this is consistent with CT Practice Book 25-60).
Unlike civil cases, Court records in criminal cases are presumed to be accessible to the public, except under limited situations including a statute, rule, regulation, or Chief Justice Directive. But even for records with an exception to public disclosure, it has to be in the form least restrictive such as redacting all or part of the record. Generally, to make criminal records inaccessible to the public, a Motion must be filed with the Court, served on the opposing party, and made public in the Public Register of Actions.
If after the Motions hearing, the Court grants the Motion, not making the record accessible can't be indefinite, and an expiration date for the Order is required. Any extension of the expiration date would also require a Motion filed, served on the opposition, and the hearing date made public. Since the Motion and hearing dates are required to be public records, information about specific court records ruled inaccessible to the public is generally available in the Register of Actions (ROA) for a case.
Family Matters
Evaluation or Studies:
Closed, except to parties and counsel (unless otherwise ordered by court).
Practice Book 25-60
Files (Civil/Family)
Open, unless sealed by court order.
Civil file and documents are available to the public when the clerk receives them officially by time-stamping the documents.
Files (Criminal)
Open, unless sealed.
Available upon filing. In cases with a great degree of public interest where a high demand is expected, the clerk should make extra copies of the documents and have them available at the counter or make multiple copies for distribution upon payment of a fee.