The current best theory for describing elementary particles and their interactions, the Standard Model, has charge-parity (CP) violation as a fundamental feature, which implies that particles and antiparticles behave differently. Due to CP violation, the decay of a meson into a certain final state might then be distinct from the decay of the anti-meson to that charge conjugated final state. This effect has been extensively studied and measured over the years in the decays of K and B mesons, which involve the strange and beauty quarks respectively, but only recently observed in D meson decays, involving the charm quark. The predicted CP asymmetries in the charm sector are very small, so, in order to make new observations, large data samples are required. This dissertation reports the search for CP violation in the singly- Cabibbo-suppressed Ds+ -> K-K+K+ and doubly-Cabibbo-suppressed D+ -> K-K+K+ decays. The search for local asymmetries in the phase space of the decays is performed with a model-independent technique, using the data samples obtained in pp collisions with a centre-of-mass energy of 13 TeV, collected by the LHCb detector during 2016—2018 (run 2). Also included is a study of the method s sensitivity to CP violation effects in the current statistics using simulations. In this analysis, two Cabibbo-favoured decays, Ds+ -> K-K+pi+ and D+ -> K-pi+pi+, are used to ensure we are not sensitive to nuisance asymmetries, from production or detection effects.