The Mugshot was most likely made by a state employee in the course of their work.
Employees don't get a copyright for works from their work but their employers do so generally, as that is work for hire. However, the government is different:
- The US government specifically can't have any copyright from works of its employees. They are public domain. 17 USC 101 & 105
- State governments are a little different. Technically they could be copyrighted unless they are laws and edicts, but states might disclaim such:
- Arizona employees make Arizona copyrighted works.
- California works require public access and are public domain unless the state specifically authorizes a work to be copyrighted.
- Florida and its employees can't have copyright in government works unless they specifically make a law that carves a work out from this beforehand.
- Indiana employees make technically copyrighted works, but they can't restrict use by obtaining a license or fee in any way under IC 5-14-3, making them quasi-public domain.
A public domain image can be done with whatever you want. No strings attached, no rights of rightsholders violated.
However, not everything made on behalf of the government is made by the government: Contractors do have the copyright in the first place, and then can assign it to a government, which does not make a work public domain.