The Cs(6D(3/2))+H-2-->CsH [X (1)Sigma(+) (nu"=0,1; J")]+H photochemical reaction has been studied in a crossed-beam experiment with electronic excitation of Cs atoms and laser-induced fluorescence detection of CsH products. The reactive cross section is measured at a collision energy of 0.09 eV: sigma(6D(3/2))=0.04x10(-16) cm(2). The rotational distributions of CsH products measured on nu"=0 for 0 less than or equal to J"less than or equal to 23 and on nu"=1 for 0 less than or equal to J"less than or equal to 15 are close to statistical ones with 16% of products in nu" =1. A quasi-classical 3D trajectory calculation of this reaction yields both rotational and vibrational distributions of CsH products and their angular scattering probability. The reactive cross section measured with Cs(6D(3/2)) excitation is an order of magnitude smaller than the cross section sigma(7P(1/2))=0.63x10(-16) cm(2), which is re-evaluated in this article.