A Tennessee legislator has proposed a statute that would outlaw the publication of gun carry permit records:
(x) Any information or other records regarding an applicant or permit holder may be released to a law enforcement agency for the purpose of conducting an investigation or prosecution, or for determining the validity of a permit, but shall not be publicly disclosed except as evidence in a criminal proceeding.
(y)(1) Except as provided for in subsection (x), it is an offense for a person, other than the applicant or permit holder, to knowingly publish in any form any information or records described in subsection (w) or information concerning the validity of any permit.
(2) A violation of this subsection (y) is a Class A misdemeanor punishable by fine only.
Nothing in the First Amendment stops states from keeping these sorts of records private. That, for instance, is the norm with regard to income tax records, to psychiatric and medical records kept by government-run hospitals, and a good deal of other data. And the government may criminalize government officials' leaking of the records, as the federal government has done for income tax records.
But once the data is placed in the public record and then copied by private parties -- which is what happened in Tennessee, prompting this proposal -- the First Amendment protects people's right to redistribute it. Florida Star v. B.J.F., a case involving the inadvertent release of a rape victim's name, so holds; and if this is so as to data that was inadvertently released by the government, it would surely apply to data that was deliberately released, even pursuant to a policy that was later changed. So the law could bar the release of new license records, but it can't bar the continuing distribution of old license records by those who have already copied them.