1. Sir, the coverage under ESI Act, 1948 is of 2 types. 1st under section 1(3) by the Central Govt.in respect of factories employing 10 or more persons. In this categories, I think, the private hospitals having their repairing workshops and doing manufacturing process etc. will also qualify as "factory" and covered/coverable under said Act.
2. 2nd category is of selected establishments under section 1(5) of said Act by appropriate State Government and in this category, I think, the State Govt. of Maharashtra had issued notification long ago covering certain establishments employing 20 or more employees. I am doubtful about whether in State of Maharashtra private hospitals have been included in said category or not. In majority of States in India( except I think Maharashtra and 2-3 other States) the appropriate State Governments have issued notifications extending the provisions of said Act to private Hospitals employing 10 or more persons.
3. This thread appears to be very old. Therefore, I will suggest to the initiator of this thread to please approach appropriate Regional/Divisional Office of ESIC in the jurisdiction of which his establishment is located and get the desired information by indicating the nature of working and employment in his establishment. The information can also be obtained through RTI.