N.Y. Comp. Codes R. & Regs. tit. 15 § 31.3
If such certificate is being filed to show that an additional vehicle or liability coverage is being added to an already existing policy, the policy period to be shown on the certificate should commence with the date upon which the policy becomes effective as to such additional vehicle or coverage. The period in which the certificate must be filed, as required by section 31.2 of this Part, will commence on the date upon which the policy becomes effective as to such additional vehicle or coverage.
Example:
A has two cars, one insured in X Company under a policy with a policy period from 7/1/64 to 7/1/65, the other in Y Company under a policy with a policy period from 8/1/63 to 8/1/64. As of 8/1/64, the second vehicle is added to the policy with X Company. The certificate of insurance to be filed by X Company with respect to the additional car should show a policy period from 8/1/64 to 7/1/65. Such certificate must be filed with the Department of Motor Vehicles within 14 calendar days after 8/1/64.
N.Y. Comp. Codes R. & Regs. Tit. 15 § 31.3