We present the first optical and infrared polarimetric study of the low mass transient X-ray binary Cen X-4 during its quiescent phase. This work is aimed to search for an intrinsic linear polarisation component in the system emitted radiation that might be due, e.g., to synchrotron emission from a compact jet, or to Thomson scattering with free electrons in an accretion disc. Multiband (BVRI) optical polarimetric observations were obtained during two nights in 2008 at the ESO La Silla 3.6 m

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... escope (EFOSC2) in polarimetric mode. These observations cover about the 30% of the 15.1 hours orbital period. J-band observations were obtained in 2007 with the NICS (TNG) instrument at La Palma, for a totality of 1 hour observation. We obtained 3-sigma upper limits to the polarisation degree in all the optical bands, with the most constraining one being in the I-band (P<0.5%). No phase-correlated variability has been noticed in all the filters. The J-band observations provided a 6% upper limit on the polarisation level. The constraining upper limits to the polarisation in the optical allowed us to evaluate the contribution of the possible emission of a relativistic particles jet to the total system radiation to be less then the 10%. This is in agreement with the observation of a spectral energy distribution typical of a single black body of a K-spectral type main sequence star irradiated from the compact object. Due to the low S/N ratio it was not possible to investigate the possible dependency of the polarisation degree from the wavelength, that could be suggestive of polarisation induced by Thomson scattering of radiation with free electrons in the outer part of the accretion disc. Observations with higher S/N ratio are required to examine in depth this hypothesis, searching for significant phase-correlated variability.