I have a Mat-Su Borough library card that includes the Palmer library. I couldn't tell you what the local laws say about this. My feeling is that the library is free and public, and if the network is unsecured, it's his to use. I'm basing this on the library being being a tax-payer supported public service.
Whether or not it is unethical or illegal to tap into a private wireless network is another question.
It could be verboten under Federal law under some provision having to do with security of computer systems, but if the Alaska police agency involved isn't Federally deputized that matter is out of their bailiwick, as it were.
I haven't heard of anything like this happening on the hard wired World Wide Web, where someone who put their server on the web, without meaning to but also without posting a warning against access, got a crime charged against someone who brought up a web page on their site. The Federal provision would require some sort of warning, if applied to the hard wired Web.
State law could be anything.