Very little is known about the polarimetric properties of CH stars and carbon-enhanced metal-poor (CEMP) stars, although many of these objects have been studied in detail both photometrically and spectroscopically. We aim to derive polarimetric properties for a large sample of CEMP stars and CH stars to fill this gap. Multiband polarimetric observations were conducted in the first run for a sample of twenty-nine objects that include twenty-two CEMP and CH stars and seven polarization standards. Estimates of polarization were obtained using standard procedures of polarization calculation. Five objects in our sample do not show any significant polarization over the different colours of BVRI. For the rest of the objects the derived percentage polarization estimates are less than or equal to 1%, and they are found to exhibit random behaviour with respect to the inverse of the effective wavelength of observations. Polarization also does not seem to have any correlation with the effective temperatures of the stars. Our polarimetric estimates indicate there are circumstellar envelopes around these stars that are spherically symmetric or envelopes with little or no dust. In the plane of differential polarization, defined as the difference between the maximum and the minimum polarizations within the BVRI-bands, versus their visual magnitude, the stars appear to be confined to a narrow band. The implication of this trend for understanding the nature of the circumstellar environment remains to be determined and requires detailed modelling.