neutrino problem*]{}, the observation of -decay combined with data on the neutrino masses from [$\mbox{}^3 {\rm H}$ $\beta$-decay ]{}experiments could provide, in principle, unique information on the CP-violation due to the Majorana CP-violating phases. As a more detailed study showed [@BPP1], information on the CP-violation of interest, and if CP-invariance holds — on the relative CP-parities of the massive Majorana neutrinos, could be obtained as well from a measurement of supplemented by information on the type of the neutrino mass spectrum (or the lightest neutrino mass $m_1$). The problem of interest was studied in detail for the QD neutrino mass spectrum (taking into account the relevant nuclear matrix element uncertainties) in [@WR00]. Further analysis [^6] showed [@PPW] that a measurement of alone could exclude the possibility of both Majorana CP-violating phases $\alpha_{21}$ and $\alpha_{31}$ being equal to zero. However, such a measurement cannot rule out without additional input that the two phases take different CP-conserving values. The additional input needed for establishing CP-violation could be, e.g., the measurement of neutrino mass $m_{\bar{\nu}_e}$ in [$\mbox{}^3 {\rm H}$ $\beta$-decay ]{}experiment KATRIN [@KATRIN], or the cosmological determination of the sum of the three neutrino masses [@Hu99], $\Sigma = m_1 + m_2 + m_3$, 