The tax imposed under the estate tax law of this state in respect of personal property (except tangible personal property having an actual situs in this state) shall not be payable (a) if the transferor at the time of his death was a resident of a state or territory of the United States, or the District of Columbia, which at the time of his death did not impose a death tax of any character in respect of personal property of residents of this state (except tangible personal property having an actual situs in such state, territory or district), or (b) if the laws of the state, territory or district of the residence of the transferor at the time of his death contained a reciprocal exemption provision under which nonresidents were exempted from said death taxes of every character in respect of personal property (except tangible personal property having an actual situs therein), provided that the state, territory or district of the residence of such nonresident decedents allowed a similar exemption to residents of the state, territory or district of residence of such decedent.