Final answer:
The person responsible for working with case managers to determine admission appropriateness is employed in the Utilization Review Department. This department ensures the effective use of hospital services and adherence to insurance policies.
Step-by-step explanation:
The appropriate hospital department for someone responsible for working with case managers of insurance companies to determine the appropriateness of admissions is the Utilization Review Department (A). This department plays a crucial role in assessing patient care requirements and ensuring that hospital services are being used effectively. They collaborate with insurance providers, case managers, and healthcare professionals to ensure that each patient's treatment is both necessary and aligns with the insurance coverage policies.