It depends upon the factual legal position as to which government is designated as the "Appropriate Government" under the particular enactment applicable to your industrial establishment. As you are aware, labor is a subject matter of the concurrent list of the Constitution enabling both the Central and State Governments to legislate appropriate laws. The term "Appropriate Government" specifically mentioned in certain labor legislations enacted by the Central Government refers to the "Government" vested with the responsibility of administration/enforcement of the concerned laws over certain establishments by virtue of their constitution or specific activity or location.
Examples of Appropriate Government Designation
For example, the Industrial Employment (Standing Orders) Act, 1946, the Industrial Disputes Act, 1947, the Contract Labor (Regulation & Abolition) Act, 1970, the Payment of Gratuity Act, 1972, the Equal Remuneration Act, 1976, the term appropriate government is defined. For the sake of quick and easy understanding, if an industrial establishment is created by a specific Central Legislation or it is a Central Government undertaking, the appropriate government to that establishment is the Central Government - e.g., Indian Railways, L.I.C of India, Unit Trust of India, BHEL, BEL, Nationalized Banks, etc.
Criteria for Determining Appropriate Government
The next criterion is with reference to the specific activity such as Postal and Telecommunications, mining, exploration of oils and minerals, etc.; yet another criterion is with reference to the territorial jurisdiction of administration - e.g., establishments situated in Union territories. For all other establishments, it is the State Governments within whose territorial jurisdiction they are functioning.
Regards, Amit