  The integrated cross section $\widetilde\sigma$ for a special type of double
polarized proton-deuteron scattering constitutes a null test
forvtime-invariance violating but P-parity conserving effects. Using the
Glauber theory for the $pd$ elastic scattering and different types of
phenomenological T-odd P-even NN-interactions we show that the contribution of
the lowest mass meson exchange, i.e. the $\rho$-meson, to the null-test signal
$\widetilde\sigma$ vanishes. Variation of the cross section $\widetilde\sigma$
due to strong hadronic and Coulomb interaction is studied and its energy
dependence is calculated in the GeV region.
