Using the truncated diagonalization method with a second-order energy correction in a B-spline basis, energies, autoionization and radiative rates are obtained for 2lnl' (n<or=7) and 3lnl' (n<or=5) singlet terms in the doubly excited He-like carbon ion and compared with experimental as well as other theoretical results where available. Branching ratios for radiative decay are determined in order to estimate the importance of radiative decay in the interpretation of ejected-electron spectra. For a proper determination of cross sections for resonant transfer excitation or double capture into 2lnl' states, it is found that it is necessary to take radiative decay into account. For the determination of cross sections for double capture into 3lnl' levels, the probability of radiative decay cannot be neglected entirely, although it is much less significant than for 2lnl'. For the latter configuration radiative decay is the dominant decay mode for most terms with n equal to or larger than 6.