The finding of nonlinear nanometric-sized probes is of key importance for the development of nonlinear microscopy in physical as well as biological sciences. We isolate nonlinear KTiOPO4 nanocrystals and study them by second-harmonic generation microscopy (SHGM) and atomic force microscopy (AFM) independently. With both polarization analysis and defocused imaging of the emitted second harmonic field, we extract the Euler angles of the crystalline axes of a single nanocrystal. A balanced coherent optical homodyne detection shows the coherent nature of the nanocrystal nonlinear emission and allows a phase measurement of the emitted second-harmonic field. These features make the KTiOPO4 nanocrystal a good candidate for a vectorial probe of electromagnetic near fields.