If my organization qualifies as a hospital for Schedule A purposes and thus as a public charity, is it required to file Schedule H?
Not necessarily. The definition of a hospital for Schedule H purposes is different than the definition of a hospital for Schedule A purposes. Schedule H must be filed by an organization that operates at least one facility that is, or is required to be, licensed, registered or similarly recognized by a state as a hospital. A hospital for Schedule A purposes is, generally, an organization whose main purpose is to provide hospital or medical care, but it does not have to be licensed, registered or similarly recognized by a state as a hospital. See Code sections 509(a)(1) and 170(b)(1)(A)(iii) and Regulations section 1.170A-9(d).