Firstly, there are no legal complications as such that one must understand. Thereafter, every state has an act available on the e-governance website outlining the exceptions and requirements for organizations to follow. Ideally, a national holiday means that the company shall remain closed, and regular functions would not be available. However, essential services might remain operational depending on the organization's work scenario.
Furthermore, if an employee works on a holiday, they are entitled to additional pay for the day or may be given a compensatory day off according to the organization's policies. If overtime (OT) is applicable, double OT is generally granted, but this also depends on the organization's policies, which should be fair and flexible.
Employees are the most important asset for any organization. Each employee is also responsible for completing tasks assigned by the organization. Managers can prepare a work chart based on job requirements to decide how to utilize subordinates and whether to call them in to work on holidays. However, this should be done within the limits of the organization and without abusing power.