If any sales tax, use tax, or motor vehicle excise tax has been paid on a motor vehicle in any other state, or political subdivision thereof, in respect to its sale or use in an amount less than the tax imposed by this chapter, the provisions of this chapter apply, but in an amount equal to the difference between the tax imposed by this chapter and the tax paid in the other state, or political subdivision thereof. If the tax paid in the other state, or political subdivision thereof, is the same or more, then no tax is due on the motor vehicle. The provisions of this section apply only if the other state, or political subdivision thereof, allows a tax credit with respect to the excise tax imposed by this chapter which is substantially similar in effect to the credit allowed by this section. The tax commissioner may require the purchaser to provide written proof from the other state, or political subdivision thereof, that the tax was legally due and paid. For purposes of this section, “state” means a state, territory, or possession of the United States, the District of Columbia, or the Commonwealth of Puerto Rico.