A nonresident individual, who at no time during the taxable year was a resident of this state, is hereby relieved of filing an income tax return to this state for that taxable year provided:
(1) His only income from sources within this state was from salaries, wages, or compensation for personal services performed within this state, and
(2) Such salaries, wages or compensation for personal services were subject to income taxation by the state of his residence under a net income tax law substantially similar in principle to this article, and
(3) The laws of such other state contain a provision substantially similar in effect to that contained in section forty of this article and applicable to residents of this state, and
(4) The laws of such other state afford like treatment to a resident of this state who earned salaries, wages or compensation for personal services in such other state.
This section shall apply with respect to taxable years beginning after December thirty-one, one thousand nine hundred sixty-three.