  The limits on time-reversal invariant tensor-type weak currents from nuclear
and neutron $\beta$ decays are evaluated including most recent experimental
data. We find that $ -0.14 \times 10^{-2} < (C_T + C^\prime_T)/C_A < 1.4 \times
10^{-2} $ and $ -0.16 < (C_T - C^\prime_T)/C_A < 0.16$ (90% C.L.), while for
the case $C_T = C^\prime_T$ the limits are $ | C_T/C_A | < 3.7 \times 10^{-3}
$. These limits are shown to be more stringent than those from recent
measurements of the radiative pion decay. In addition, the sensitivity of
future $10^{-3}$-level correlation measurements is investigated.
