N.Y. Comp. Codes R. & Regs. tit. 20, § 484.3 – Interchanged equipment.

(a) If motor vehicles for which permits were issued to the taxpayer are operated by another carrier who will pay the tax, form TMT-4 (Equipment Interchanged or Leased) must be filed with the tax return on form MT-903.
(b) If the owner of a motor vehicle has obtained a permit and sticker therefor and leased or interchanged it during the reporting period to different carriers who operate the motor vehicle under the owner's permit, such motor vehicle must be reported by the owner in either of the following ways:
1. (1) If the owner pays the tax, the motor vehicle should be reported on the tax return of the owner on form MT-903.
2. (2) If the lessee will pay the tax, the owner should file form MT-903 accompanies by form TMT-4. Form MT-903 will be filled in only to the extent of the heading and the certification. Form TMT-4 will list the permit number of each vehicle, the unloaded and maximum gross weights indicated on such permit, the name and address of the lessee, and such other information as may be required. The lessee must report such vehicle on his own tax return.
(c) If the owner of a motor vehicle has obtained a permit and sticker therefor and it is subsequently leased to a lessee who obtains a permit, the owner should list such motor vehicle on form MT-903 with a notation, “Leased to and reported under permit number of (name of lessee)”. The lessee will account for such vehicle under his own permit number. Should the owner wish to relieve himself of the responsibility of reporting such motor vehicle on each tax return, he may do so by surrendering his permit to the Miscellaneous Tax Bureau for cancellation and by destroying the sticker.
(d) A lessee of a motor vehicle who has obtained a permit therefor must include said motor vehicle on his tax return until he surrenders the permit and plate.
(e) Carriers interchanging or leasing equipment are required to give each other the necessary mileage information and the unloaded and maximum gross weight of the vehicle involved.
Example:
Permits for Tractor A and Trailer B have been issued to Smith Truck Company, which operates Tractor A and Trailer B from Albany to Poughkeepsie, where Trailer B is interchanged with Trailer C (for which a permit has been issued to Jones Transportation Company). Tractor A and Trailer C continue on to New York City, and Trailer B and Tractor D return to Albany. (The permit for Tractor D has been issued to Jones Company.)
Smith Truck Company must file a tax return reporting on the mileage of Tractor A and Trailer B from Albany to Poughkeepsie and on Tractor A and Trailer C from Poughkeepsie to New York City. Smith Truck Company may also include in its return, the mileage of Tractor D and Trailer B from Poughkeepsie to Albany, or it may file from TMT-4 indicating that Trailer B was interchanged with Jones Transportation Company.
If Smith Truck Company files form TMT-4, Jones Transportation Company must report on the mileage of Tractor D and Trailer B. Jones Transportation Company must also file form TMT-4 indicating that Trailer C was interchanged with Smith Truck Company.