[en] We present results for the renormalization constants of bilinear quark operators obtained by using the tree-level Symanzik improved gauge action and the N_f=2 twisted mass fermion action at maximal twist, which guarantees automatic O(a)- improvement. Our results are also relevant for the corresponding standard (untwisted) Wilson fermionic action since the two actions only differ, in the massless limit, by a chiral rotation of the quark fields. The scale-independent renormalization constants Z_V, Z_A and the ratio Z_P/Z_S have been computed using the RI-MOM approach, as well as other alternative methods. For Z_A and Z_P/Z_S, the latter are based on both standard twisted mass and Osterwalder-Seiler fermions, while for Z_V a Ward Identity has been used. The quark field renormalization constant Z_q and the scale dependent renormalization constants Z_S, Z_P and Z_T are determined in the RI-MOM scheme. Leading discretization effects of O(g²a²), evaluated in one-loop perturbation theory, are explicitly subtracted from the RI-MOM estimates. (orig.)