  Let X be a multi-type continuous-state branching process with immigration
(CBI process) on state space $\mathbb{R}^d$. Denote by $g_t$, $t \geq 0$, the
law of $X_{t}$. We provide sufficient conditions under which $g_t$ has, for
each $t > 0$, a density with respect to the Lebesgue measure. Such density has,
by construction, some anisotropic Besov regularity. Our approach neither relies
on the use of Malliavin calculus nor on the study of corresponding Laplace
transform.
