The Baxter County Quorum Court is composed of 11 members called Justices of the Peace. These Justices of the Peace are district officers and not county officials because they represent a district within the county. Justices of the Peace are elected to two-year terms. These district officials meet each month, more often if necessary, to conduct county business and review ordinances and resolutions for passage. All powers not vested in the County Judge as the Chief Executive Officer of the county shall continue to be exercised and administered by the county court, over which the County Judge shall preside. The county court, in fact, is the County Judge sitting in a judicial role. The County Judge does not have a vote but does have the power of veto. This veto can be overridden with a 3/5ths vote of the total membership of the Quorum Court.

The county court of each county has exclusive original jurisdiction in all matters relating to County Taxes, including real and personal ad valorem taxes collected by county government. The county court's authority in this area includes jurisdiction over the assessments of property, equalization of assessments on appeal, tax levies, tax collections, and the disbursement of tax proceeds. The court also has original jurisdiction in all matters relating to paupers. The court's jurisdiction includes all county administrative actions affecting the conduct of human services programs serving indigent residents of the county where such services are financed in total or in part by county funds.

And the county court has jurisdiction in each other case that may be necessary to the internal improvement and local concerns of the respective counties, including county financial activities and works of general public utility or advantage designed to promote intercommunication, trade and commerce, transportation of persons and property, or the development of natural resources, which are not otherwise transferred to the County Judge to be administered in an executive capacity.