How do you divide the roles between HR and the Health Manager when a report of employee suicide risk is received?

Hello, I am handling both EAP and employee health management at my company.
Recently, an employee informed HR that a colleague was repeatedly talking about suicide.
Fortunately, it was not an immediate emergency, but it was mentioned that there are no clear internal guidelines on whether HR should contact someone first or pass the matter directly to the health manager when such a report is received.
HR may need to handle attendance, contact guardians, or take company-level measures.
It seems like health managers should be responsible for checking health status and coordinating with hospitals and EAP, but it is unclear at what stage and who is actually in charge.
Especially when contacting employees, having multiple departments call separately would likely be burdensome, so I think it would be better for one person to act as the central point of contact.
In such cases, how do you divide the roles, from receiving the initial report and verifying the risk level to contacting guardians or external agencies, connecting with an EAP, and subsequently managing attendance or leave of absence?
Also, since information regarding suicide risk is sensitive, I am wondering to what extent HR is permitted to record and share it.
I am curious how those of you operating crisis response processes at your companies differentiate the roles of HR and health managers.