Let's not get overly excited over an innocent mistake
Facebook needs to allow "business" accounts, so an office can manage a page without people having to use their personal profiles.
The lead headline in Thursday's Herald-Times was about a mistaken post on Facebook that was deleted after a few hours, along with a discussion of possible criminal penalties for the mistaken post. (A city employee shared a post from the incumbent mayor's campaign page to city government's official Facebook page.) In addition to the observation that it must have been a slow news day, we need to get some perspective.
I manage three pages on Facebook. It is relatively easy to "share" something to the wrong page, or to a page instead of a personal profile, especially when using a smartphone instead of a desktop PC. That does not excuse sharing things to an inappropriate location, and it is important to be careful when managing an official government page, but it is easy to see how a mistake like that gets made.
This almost certainly was an accident, not an intentional misuse of an official city government page for a political campaign. She was not on the clock. She should get an informal verbal reprimand, that's it.
Facebook needs to allow "business" accounts, so an office can manage a page without people having to use their personal profiles. As it is now, people have to use personal profiles to manage Pages. I guarantee you at larger organizations there are people with dummy accounts that technically break Facebook's rules to manage pages. Technically you are only allowed to have one account. That is a stupid rule that does not match the needs of large organizations. There needs to be exceptions to the "one account" limit.
There certainly should not be criminal charges against the staffer for making an innocent mistake on her own time. Even if one could argue she should face professional consequences for her mistake (which I disagree with, as I explained above) criminal charges would be obscene.