The azimuthal asymmetry and the transverse momentum of forward produced charged hadrons in deep inelastic muon scattering have been studied as a function of the event kinematics and of the hadron variables. Primordial $k_T$ of the struck parton and O($alpha_s$) corrections to the cross-section are expected to contribute to the transverse momentum and the azimuthal asymmetry of hadrons. The data show some unexpected dependences not present in a Monte Carlo simulation which includes the theoretical parton-level azimuthal asymmetry.