No person shall participate in an advanced dental education program unless he has received a permit issued by the Department of Public Health. The permit shall be issued solely for purposes of participation in an advanced dental education program conducted by a dental or medical school or by a hospital operated by the federal government or licensed pursuant to subsection (a) of section 19a-491. No person shall receive a permit until a statement has been filed with the department on his behalf by the program administration certifying that he is to be enrolled in the program and that he has received the degree of doctor of dental medicine or doctor of dental surgery or its equivalent.