Wis. Stat. § 48.035
Menominee County is attached to Shawano County for judicial purposes to the extent of the jurisdiction and functions of the court assigned to exercise jurisdiction under this chapter and ch. 938 and the office and functions of the judge of the court, and the duly designated judge of the court assigned to exercise jurisdiction under this chapter and ch. 938 of the circuit court for Menominee and Shawano counties shall serve in both counties. The county boards of Menominee County and Shawano County shall enter into an agreement on administration of this section and the prorating of expenditures involved, and for such purposes the county board of supervisors of Menominee County may appropriate, levy and collect a sum each year sufficient to pay its share of the expenses. If the 2 county boards are unable to agree on the prorating of expenditure involved, then the circuit judges for the circuit court for Menominee and Shawano counties shall, upon appropriate notice and hearing, determine the prorating of the expenditures on the basis of a fair allocation to each county under such procedure as they prescribe. If the circuit judges are unable to agree, the chief judge of the judicial administrative district shall make the determination.
Wis. Stat. § 48.035