We present an analysis of the main mechanisms of dissipation of resonant multilayer double-clamped microbeams in the frequency range 200 to 500 kHz. The devices consist of 2μm thick silicon nitride (E ≈ 160 GPa) beams covered with a polymer IP-Dip (E ≈ 4 GPa) layer fabricated by two-photon polymerization. A laser-Doppler vibrometer was used to measure the resonant vibrations and energy dissipation of the devices in high vacuum (< 0.05 Pa) at room temperature. The experimental findings were compared with theoretical and finite element method (FEM) results. The quality factor, dominated by the intrinsic dissipation in the IP-Dip layer, has proven to have a strong dependence on polymer thickness. On this basis, a viscous model for intrinsic dissipation in a polymer layer was formulated.