Researchers proposed CRC-Router, a risk-constrained routing module for medical AI. It combines uncertainty signals with predictive scores to estimate wrong-accept risk. The module uses Conformal Risk Control to calibrate acceptance thresholds. It works with both conventional models and agentic medical AI systems. CRC-Router was tested on chest X-ray triage using the NIH ChestX-ray14 dataset. It achieved the strongest risk-coverage trade-off among evaluated baselines. It can be used as a standalone layer or integrated with MedRAX. Code is publicly available. The paper was submitted to arXiv on 25 September 2026.