Any aircraft of which a nonresident has the right to possession and which is used for commercial operations in this state shall be registered in this state before said aircraft is used for such commercial operations, except that aircraft used for charter which a nonresident has the right to possession need not be so registered if while in the state the nonresident does not advertise, represent, or hold out as giving or offering to provide such service with such aircraft. Aircraft registered under this section shall not be entitled to a refund under 360.62 except if destroyed or for errors in computing the tax or fees and for the error on the part of an owner who may have registered an aircraft that was not before or at the time of such registration, or at any time thereafter during the current past year, subject to such tax in this state, or the aircraft is sold to a nonresident who is not engaged in a commercial operation in this state.