We considered the problem of a two-legged bosonic ladder with a single impurity correlated across the rungs of the ladder, i.e. an impurity that is coupled to the density of both legs at the same point. We studied the problem at absolute zero temperature and in the limit in which the impurity potential is the smallest energy scale of the problem, using a bosonization scheme. A renormalization group procedure determined the existence of a regime in which the antisymmetric modes become massive, and of another one in which they remain massless. For both regimes, a transition between conducting and insulating behaviours has been found, determined, in this limit, only by the interactions and not by the strength of the impurity. In the massless regime, the transition takes place at $K_s+K_a=2$, while in the massive regime it occurs at $K_s=2$ for attractive interchain coupling and $K_s=1/2$ for repulsive coupling, $K_s$ and $K_a$ being the Luttinger liquid parameters of the symmetric and the antisymmetric modes of the ladder. Several comparisons between the bosonic ladder and a single chain have also been discussed.