They had a contract with some office in the state government. The courthouse is owned by a county, as most courthouses in USA are. Later the fig-leaf of "they use a state-administrated computer program there" was constructed so as to limit the injustice inflicted on two humans, but county buildings are no more owned by the state than state buildings are owned by the feds.

And yes, stipulated, the sheriff is an asshole, but even he would have honored a contract between Coalfire and Dallas County, Iowa.