The adoption of machine-learning-enabled systems in the healthcare domain is on the rise. While the use of ML in healthcare has several benefits, it also expands the threat surface of medical systems. We show that the use of ML in medical systems, particularly connected systems that involve interfacing the ML engine with multiple peripheral devices, has security risks that might cause life-threatening damage to a patient's health in case of adversarial interventions. These new risks arise due to security vulnerabilities in the peripheral devices and communication channels. We present a case study where we demonstrate an attack on an ML-enabled blood glucose monitoring system by introducing adversarial data points during inference. We show that an adversary can achieve this by exploiting a known vulnerability in the Bluetooth communication channel connecting the glucose meter with the ML-enabled app. We further show that state-of-the-art risk assessment techniques are not adequate for identifying and assessing these new risks. Our study highlights the need for novel risk analysis methods for analyzing the security of AI-enabled connected health devices.