"Public domain" refers informally to copyright status, usually works whose protected status has expired. A list of names, addresses and criminal offenses is "factual", not a creative expression, and is not subject to copyright protection. You may be thinking of "public record", which is closer to an relevant expression. Typically, as instantiated in Washington state under RCW 9a.44.130 ff, a person convicted of certain offenses is required to register with the county sheriff, and that registration is thus a "public record". Under a separate law, RCW 4.24.550 disclosure is allowed "when the agency determines that disclosure of the information is relevant and necessary to protect the public and counteract the danger created by the particular offender" – in other jurisdictions disclosure may be mandatory. The specific information to be disclosed is "name, relevant criminal convictions, address by hundred block, physical description, and photograph. The website shall provide mapping capabilities that display the sex offender's address by hundred block on a map". The Public Records Act does not exclude disclosure and copying of that information, so it is a public record in the sense that it must be disclosed on request.
Every state has its own laws implementing this desideratum: all states have such laws, they vary somewhat in details.