This isn’t even technically legal. What u said is all wrong actually. U should ALWAYS refer the employee to HR when they are taking a bunch of time off for any medical, family, or traumatic/mental issue.
This isn't wrong at all. If the employee is staying out due to "mental distress" and the employee does not come to work after a few days, the manager has every right to ask the employee if she has a medical note supporting her leave of absence.
Especially in light of her potentially bullshytting about the seriousness of everything.
Yes, HR can be involved, but they would likely ask the same thing before it turns into an employee relations issue if this keeps dragging out.
If the restaurant as a personal leave of absence policy, that could be applied here depending on the circumstances and eligibility requirements if she's going to claim mental stress but won't see a doctor.