  In this note we extend to the quasi-reflexive setting the result of F.
Baudier, N. Kalton and G. Lancien concerning the non-embeddability of the
family of countably branching trees into reflexive Banach spaces whose Szlenk
index and Szlenk index from the dual are both equal to the first infinite
ordinal $\omega$. In particular we show that the family of countably branching
trees does neither embed into the James space $\mathcal{J}_p$ nor into its dual
space $\mathcal{J}_p^*$ for $p\in(1,\infty)$.
