The shape of a neutron star (NS) is closely linked to its internal structure and the equation of state of supranuclear matters. A rapidly rotating, asymmetric NS in the Milky Way undergoes free precession, making it a potential source for multimessenger observation. The free precession could manifest in (i) the spectra of continuous gravitational waves (GWs) in the kilohertz (kHz) band for ground-based GW detectors, and (ii) the timing behaviour and pulse-profile characteristics if the NS is monitored as a pulsar with radio and/or X-ray telescopes. We extend previous work and investigate in great detail the free precession of a triaxially deformed NS with analytical and numerical approaches. In particular, its associated continuous GWs and pulse signals are derived. Explicit examples are illustrated for the continuous GWs, as well as timing residuals in both time and frequency domains. These results are ready to be used for future multimessenger observation of triaxially deformed freely precessing NSs, in order to extract scientific implication as much as possible
