Where a local sales or use tax has been paid with respect to tangible personal property by the purchaser either in another local tax jurisdiction within the state or in a tax jurisdiction outside the state, the tax may be credited against the tax authorized to be imposed by this article upon the same property. If the amount of sales or use tax so paid is less than the amount of the use tax due under this article, the purchaser shall pay an amount equal to the difference between the amount paid in the other tax jurisdiction and the amount due under this article. The commissioner may require such proof of payment in another local tax jurisdiction as he deems necessary and proper. No credit shall be granted, however, against the tax imposed under this article for tax paid in another jurisdiction if the tax paid in such other jurisdiction is used to obtain a credit against any other local sales and use tax levied in the special district or in the county which is coterminous with the special district; and taxes so paid in another jurisdiction shall be credited first against the tax levied under this article and then against the tax levied under Article 3 of this chapter, if applicable.