The rovibrational state distributions for the H-2 product of the H+c-C6H12-->H-2+c-C6H11 abstraction reaction have been measured at 1.6 eV collision energy under single-collision conditions. The state distributions are compared to those for the H-2 product of the reaction of H atoms with CD3(CH2)(4)CD3 and n-C6H14 that we have measured previously. Abstraction of secondary H atoms from the cyclic C-6 alkane produces H-2(v(')=0,j(')) and H-2(v(')=1,j(')) rotational state distributions that are significantly colder than those from the reaction of the linear C-6 alkane. These results are interpreted within a simple phenomenological local reaction model that we have developed for these atom+polyatom reactions. The substantial differences between the state distributions for the reactions of the cyclic and linear alkanes indicate that reactions of cyclohexane are not representative of reactions at all secondary C-H.