Answer from Kyle, PHR:
No. If you’ve confirmed that she isn’t experiencing symptoms of COVID-19, I would recommend treating this instance of coughing as a one-off event and not indicative of the virus. You can remind her and other employees to stay home if they are experiencing symptoms, but one instance of coughing could be due to any number of factors, and in this case the employee provided an alternate explanation.
That said, if an employee were to have persistent coughing, then it would be advisable to send them home. If that employee were to claim their symptoms are from another cause (e.g., allergies, asthma, common cold), the most risk-averse response would be to send them home with pay until the symptoms resolve or they can provide evidence of the other source of the symptoms.
We also recommend that employees wear masks at work, even if not required by your state or locality. The potential risk that any employee poses to others goes down significantly if they are wearing a mask while coughing (or talking, laughing, sneezing, or simply breathing).
Kyle is a professional author, editor, and researcher specializing in workplace culture, retention strategies, and employee engagement. He has previously worked with book publishers, educational institutions, magazines, news and opinion websites, nationally-known business leaders, and non-profit organizations. He has a BA in English, an MA in philosophy, and a PHR certification.