A search is performed for rare and forbidden charm decays of the form D+-> hl+l -/+, where h(+/-) is a pion or kaon and l((')+/-) is an electron or muon. The measurements are performed using proton-proton collision data, corresponding to an integrated luminosity of 1.6 fb(-1), collected by the LHCb experiment in 2016. No evidence is observed for the 25 decay modes that are investigated and 90 % confidence level limits on the branching fractions are set between 1.4 x 10(-8) and 6.4 x 10(-6). In most cases, these results represent an improvement on existing limits by one to two orders of magnitude.