We examine, in a model independent way, the sensitivity of a linear collider to the couplings of a light Higgs boson to a pair of gauge bosons, including the possibility of CP violation. We construct several observables that probe the various possible anomalous couplings. For an intermediate mass Higgs, a collider operating at a center of mass energy of 500 GeV and with an integrated luminosity of 500 fb^-1 is shown to be able to constrain the $ZZH$ vertex at the few per cent level, with even higher sensitivity for some of the couplings. However, lack of sufficient number of observables as well as contamination from the $ZZH$ vertex limits the precision to which anomalous part of the $W W H$ coupling can be probed.