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In this paper we study local regularity for the generalized solution to the Dirichlet problem related to the equation $$Lu\equiv X_i^{*}(a_{ij}{X}_{j}u)=f.$$ where $X_1,X_2,\mathrm{\dots },X_m$ are vector fields satisfying Hörmander condition and $a_{ij}\in L^{\mathrm{\infty }}$. We give a representation formula for the generalized solution in terms of the Green function and thanks to suitable estimates we achieve our goal. In the case $f\ge 0$ we are able to give necessary condition too.