1. (a) Motor vehicles operated by the United States, New York State, or any other State, or by any county, city, town or municipality in New York State or any other State or by any agency or department thereof are exempt from the statute.
2. (b) If a motor vehicle is operated by a private person although owned by one of the foregoing it is not exempt and must have a permit. Thus a motor vehicle owned by one of the foregoing governments, agencies or departments which is leased to a private contractor is not exempt. Similarly a motor vehicle operated by a private person under a contract with any of the foregoing governments, agencies or departments is not exempt.

3. (c) However, if a motor vehicle is operated by one of the foregoing governments, agencies or departments, it is exempt from the statute even if owned by a private person.

   Example 1:

   A contractor having a cost-plus contract with the United States owns a motor vehicle which he operates in connection with such contract. The motor vehicle is required to have a permit.

   Example 2:

   A county leases a truck from a private person and the truck is operated by a county employee for purposes of snow removal. It is exempt from the statute when so used.

   Example 3:

   A county enters into an agreement with a contractor for the removal of snow from its highways under which the contractor furnishes the truck and the driver. The truck is not exempt.

Tax Law, § 504, subd. 2.