Whoever he may be, a private hospital is an establishment under the State Shops&Ests Acts. Therefore, when once the total number of employees becomes 10 or above, the Payment of Gratuity Act, 1972 would be automatically applicable to such Private Hospital by virtue of the provision of Section 1(3)(b) of the Act.
As far as I know, the issuance of appointment order to employees is not made mandatory by any Law other than the Sales Promotion Employees Act and certain States' Shops&Ests Acts. Any way, non-issue of appointment orders cannot help the employer to repudiate the claim for gratuity by an ex-employee. The employee can prove the factum of his actual length of service in the hospital by means of various other evidence like wages slips given, ECS transactions and the like.
15th September 2018 From India, Salem