We recommend that you defer to the employee’s own healthcare provider for this decision. Their provider may or may not have the employee get a COVID-19 test, and ultimately that’s between the provider and the employee.
We do recommend getting something in writing that confirms they’re able to come back to work. Tell the employee that you will need either a doctor’s note clearing them to return to work, or documentation of a negative COVID-19 test.
Just note that you cannot require that they give you a copy of test results, as that is their private medical information. But they can certainly choose to supply it.