As per Section 66D(a) of F.A'1994, service by Government or a local authority excluding the following services to the extent they are not covered elsewhere, (a) services by Government or a local authority excluding the following services to the extent they are not covered elsewhere—
(i) services by the Department of Posts by way of speed post, express parcel post, life insurance and agency services provided to a person other than
Government;
(ii) services in relation to an aircraft or a vessel, inside or outside the precincts of a port or an airport;
(iii) 5transport of goods or passengers; or
(iv) support services, other than services covered under clauses (i) to (iii) above, provided to business entities;
are in negative list hence not taxable.
Also,logically Central/State Govt. and departments are part of Union of India/States and performing their statutory duties even when they help each other, even if there are financial transaction the same can not be considered as "consideration" and the activity can not be considered as "Service" provided to another for "Consideration" hence this activity does not fall under definition "Service" as defined in Section 65B(44) of the Finance Act'1994.
The same view has been explained in para 2.4.11 of Guidance Note as under.
2.4.11 Would services provided by one department of the Government to another
Department of the Government be taxable?
If services are provided by one department of the Central Government to another department
of the Central Government or by a department of a State Government to another department
of the same State Government then such service would not be taxable as it would amount to
self-service. To be taxable a service has to be provided to another person.
On the other hand if a service is provided by a Central Government department to a State
Government department or vice versa or a by a State to another State Government or by a
Government to an autonomous body, the same would be taxable if such service does not fall
in the negative list. It is another matter that most of the services provided by the Government
are in the negative list. For details please refer to point no. 4.1 of this Guide.