Polarization measurements in
$$ \overline{B}\to {D}^{\left(\ast \right)}\tau \overline{\nu} $$
B
¯
→
D
∗
τ
ν
¯
are useful to check consistency in new physics explanations for the R
D
and
$$ {R}_{D^{*}} $$
R
D
*
anomalies. In this paper, we investigate the D
* and τ polarizations and focus on the new physics contributions to the fraction of a longitudinal D
* polarization (F
L
D *
), which is recently measured by the Belle collaboration F
L
D *
= 0.60 ± 0.09, in model-independent manner and in each single leptoquark model (R2, S1 and U1) that can naturally explain the
$$ {R}_{D^{\left(\ast \right)}} $$
R
D
∗
anomalies. It is found that ℬ(B
c
+
→ τ
+
ν) severely restricts deviation from the Standard Model (SM) prediction of F
L,SM
D *
= 0.46±0.04 in the leptoquark models: [0.43, 0.44], [0.42, 0.48], and [0.43, 0.47] are predicted as a range of F
L
D *
for the R2, S1, and U1 leptoquark models, respectively, where the current data of
$$ {R}_{D^{\left(\ast \right)}} $$
R
D
∗
is satisfied at 1σ level. It is also shown that the τ polarization observables can much deviate from the SM predictions. The Belle II experiment, therefore, can check such correlations between
$$ {R}_{D^{\left(\ast \right)}} $$
R
D
∗
and the polarization observables, and discriminate among the leptoquark models.