You can deduct the cost of a CNA that is providing medical services.
If you pay someone directly (not through an agency) to work in your home as a caregiver or housekeeper, then they are considered household employees and you are responsible for their social security taxes. Please see this TurboTax tips article for more information regarding household employees.
You can include in medical expenses - wages and other amounts you pay for nursing services. The services need not be performed by a nurse as long as the services are of a kind generally performed by a nurse. This includes services connected with caring for the patient's condition, such as giving medication or changing dressings, as well as bathing and grooming the patient.
Generally, only the amount spent for nursing services is a medical expense. If the CNA also provides personal and household services, amounts paid to the attendant must be divided between the time spent performing household and personal services and the time spent on nursing services.