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 sales and use tax may be credited against the sales and use 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 the commissioner deems necessary and proper. No credit shall be granted, however, against the sales and use tax imposed under this article for tax paid in another jurisdiction if the sales and use 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 conterminous with the special district; and sales and use taxes so paid in another jurisdiction shall be credited first against the sales and use tax levied under this article and then against the sales and use tax levied under Article 3 of this chapter, if applicable.