One of our family practice physicians shared her COVID-19 Toolkit, which includes testing protocols.
It is an individual choice of the practice as to who will collect the specimen. One practice described the process as exactly like that for a rapid flu test, so most providers and medical assistants were comfortable with the process. Some, out of concern of exposing their employees, decided only providers would collect the specimen. Other providers who believed their medical assistants were capable of collecting the specimen safely allowed them to collect. And, some providers are implementing patient self-testing.
Whatever process is implemented for your practice, it is important to train all involved employees on using PPE and the proper specimen collection process.