  The weak dipole moments of elementary fermions are calculated at the one-loop
level in the framework of a renormalizable scalar leptoquark model that forbids
baryon number violating processes and so is free from the strong constraints
from experimental data. In this model there are two scalar leptoquarks
accommodated in an $SU_L(2)\times U_Y(1)$ doublet: one of such leptoquarks is
non-chiral and has electric charge of $5/3e$, whereas the other one is chiral
and has electric charge $2/3e$. In particular, a non-chiral leptoquark
contributes to the weak properties of an up fermion via a chirality
flipping-term proportional to the mass of the virtual fermion and can also
induce a non-zero weak electric dipole moment provided that the leptoquark
couplings are complex. The numerical analysis is focused on the weak properties
of the $\tau$ lepton since they offer good prospects for their experimental
study. The constraints on leptoquark couplings are briefly discussed for a
non-chiral leptoquark with non diagonal couplings to the second and third
fermion generations, a third-generation non-chiral leptoquark, and a
third-generation chiral leptoquark. It is found that although the
chirality-flipping term can enhance the weak properties of the $\tau$ lepton
via the top quark contribution, such an enhancement would be offset by the
strong constraints on the leptoquark couplings. So, the contribution of scalar
leptoquarks to the weak magnetic dipole moment of the $\tau$ lepton are smaller
than the standard model (SM) contributions but can be of similar size than
those arising in some SM extensions. A non-chiral leptoquark can also give
contributions to the weak electric dipole moment larger than the SM one but
well below the experimental limit. We also discuss the case of the off-shell
weak dipole moments and for completeness analyze the behavior of the $\tau$
electromagnetic properties.
