Ind. Code § 6-3.5-4-3

Sec. 3. If an adopting entity adopts an ordinance imposing the surtax after December 31 but before September 1 of the following year, a vehicle is subject to the tax if it is registered in the county after December 31 of the year in which the ordinance is adopted. If an adopting entity adopts an ordinance imposing the surtax after August 31 but before the following January 1, a vehicle is subject to the tax if it is registered in the county after December 31 of the year following the year in which the ordinance is adopted. However, in the first year the surtax is effective, the surtax does not apply to the registration of a vehicle for the registration year that commenced in the calendar year preceding the year the surtax is first effective.