Does the patient monitor need an airworthiness certificate?

No need. Airworthiness certification means that equipment or components installed on civil aircraft must have certification documents that meet airworthiness standards. The patient monitor is not a device or component on a civil plane, but a medical device, which is mainly used in hospitals, clinics and other medical places to monitor the patient's vital signs and changes in his condition, so the patient monitor does not need airworthiness certification.