I think in this case, a copyright is well-justified. They have to publish the mugshot for some reasons, but without the copyright, such a mugshot could be abused. Having the copyright at least enables the government to have some control over this.
Just imagine having your mugshot taken, and it later turns out you are completely innocent. Still, if the mugshot was in the public domain, your neighbor with whom you have a dispute over the height of cut lawn could just print your face on every billboard in the country.