California version of Megan's Law orders the California Department of Justice to put on the Web information about sex offenders; but Cal. Penal Code § 290.46(j) says:

(1) A person is authorized to use information disclosed pursuant to this section only to protect a person at risk.

(2) Except as authorized under paragraph (1) or any other provision of law, use of any information that is disclosed pursuant to this section for purposes relating to any of the following is prohibited:
(A) Health insurance.
(B) Insurance.
(C) Loans.
(D) Credit.
(E) Employment.
(F) Education, scholarships, or fellowships.
(G) Housing or accommodations.
(H) Benefits, privileges, or services provided by any business establishment.
. . .

(4) (A) Any use of information disclosed pursuant to this section for purposes other than those provided by paragraph (1) or in violation of paragraph (2) shall make the user liable for the actual damages, and any amount that may be determined by a jury or a court sitting without a jury, not exceeding three times the amount of actual damage, and not less than two hundred fifty dollars ($250), and attorney's fees, exemplary damages, or a civil penalty not exceeding twenty-five thousand dollars ($25,000).

(B) Whenever there is reasonable cause to believe that any person or group of persons is engaged in a pattern or practice of misuse of the information available via the Internet Web site in violation of paragraph (2), the Attorney General, any district attorney, or city attorney, or any person aggrieved by the misuse is authorized to bring a civil action in the appropriate court requesting preventive relief, including an application for a permanent or temporary injunction, restraining order, or other order against the person or group of persons responsible for the pattern or practice of misuse. The foregoing remedies shall be independent of any other remedies or procedures that may be available to an aggrieved party under other provisions of law, including Part 2 (commencing with Section 43) of Division 1 of the Civil Code.

The California Justice Department's Megan's Law FAQ plausibly interprets this as barring people from telling others about what they learned from the Web site, as a form of "use" of the information:

I want to share with others the information I found on the Attorney General's Megan's Law Website. Does the law prohibit me in any way from sharing this information?

A person may use the information disclosed on the Attorney General's Web site only to protect a person at risk. It is a crime to use the information disclosed on the Attorney General's Internet Web site to commit a misdemeanor or felony. Unless the information is used to protect a person at risk, it is also prohibited to use any information that is disclosed pursuant to this Internet Web site for a purpose relating to health insurance, insurance, loans, credit, employment, education, scholarships, fellowships, housing, accommodations, or benefits, privileges, or services provided by any business. Misuse of the information may make the user liable for money damages or an injunction against the misuse. Before using the information disclosed on this Web site, you may want to consult with an attorney or merely suggest to others that they view the Web site for themselves.

So California law suppresses presumptively true statements of fact about criminals based on a public record, unless one's purpose is "only to protect a person at risk." If one learns that a neighbor or a coworker has committed a heinous crime, and wants to tell people -- not specifically to protect a person at risk, but (for instance) to urge people not to give a fellowship to someone with such bad morals, or to urge businesses not to associate with such an evil person -- one risks damages liability or an injunction.

Seems like a pretty clear First Amendment violation, especially given Florida Star v. B.J.F. If it's unconstitutional to bar speakers from revealing the names of rape victims when those names were accidentally released by government officials into the public record, I'd think that it would be unconstitutional to bar speakers from revealing the names of rapists when those names were deliberately placed by government officials into the public record. But it seems that California weighs the privacy of public-record information about sex criminals more heavily than its law-abiding citizens' constitutionally protected free speech.

Thanks to Cathy Seipp for the pointer.