Ind. Code § 6-3.5-5-5
If an adopting entity adopts an ordinance imposing the wheel tax after December 31 but before September 1 of the following year, a vehicle described in section 2(a) of this chapter 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 wheel tax after August 31 but before the following January 1, a vehicle described in section 2(a) of this chapter 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 tax is effective, the tax does not apply to the registration of a motor vehicle for the registration year that commenced in the calendar year preceding the year the tax is first effective.
IC 6-3.5-5-5