Ind. Code § 36-7-8-8

Sec. 8. A county that has adopted an ordinance under section 4 of this chapter may contract with any city located in the county to have the city administer and enforce that ordinance. The contract must be for a stated and limited period, and may be renewed. All actions, notices, or other writings under such a contract must be performed as the county building commissioner would perform them, and may not be performed in the name of the city.