By generating terahertz pulses in KTP crystals through optical rectification with a pump photon energy varying from below to above the bandgap, we observe a peak of the THz signal at the bandgap energy but also a second one around half the bandgap. This later one is attributed to a two-photon absorption enhanced nonlinearity, which is validated by the similarity of the two-photon absorption coefficient and THz peak amplitude data versus the pump photon energy. A careful analysis of the KTP sample absorption spectral dependence nearby the bandgap demonstrates that KTP is an indirect bandgap crystal, whose absorption below the bandgap involves emission of a phonon related to the symmetric Ti-O stretching vibration, i.e. the ν1 (A1g) mode.