Vet Connect Act of 2017 This bill authorizes the Department of Veterans Affairs (VA) to disclose to non-VA entities that provide hospital care or medical treatment to veterans (including private entities and other federal agencies) records of the identity, diagnosis, prognosis, or treatment of any patient in connection with a program relating to drug abuse, alcoholism or alcohol abuse, infection with the human immunodeficiency virus, or sickle cell anemia. Such an entity may not redisclose or use such record for a purpose other than that for which the disclosure was made.