If the taxpayer is regarded as a resident both of this state and another jurisdiction for purposes of personal income taxation, the Tax Commissioner shall reduce the tax on that portion of the taxpayer’s income which is subjected to tax in both jurisdictions solely by virtue of dual residence; Provided, that the other taxing jurisdiction allows a similar reduction. The reduction shall be in an amount equal to that portion of the lower of the two taxes applicable to the income taxed twice which the tax imposed by this state bears to the combined taxes of the two jurisdictions on the income taxed twice.