(1) Each county, city, and town is responsible for the prosecution, adjudication, sentencing, and incarceration of misdemeanor and gross misdemeanor offenses committed by adults in their respective jurisdictions, and referred from their respective law enforcement agencies, whether filed under state law or city ordinance, and must carry out these responsibilities through the use of their own courts, staff, and facilities, or by entering into contracts or interlocal agreements under this chapter to