  We report a detailed study of the ground state helical magnetic structure in
monophosphide FeP by means of ${}^{31}$P NMR spectroscopy. We show that the
zero-field NMR spectrum of the polycrystalline sample provides strong evidence
of an anisotropic distribution of local magnetic fields at the P site with
substantially lower anharmonicity than that found at the Fe site by
M\"{o}ssbauer spectroscopy. From field-sweep ${}^{31}$P NMR spectra we conclude
that a continuous spin-reorientation transition occurs in an external magnetic
field range of 4 - 7 T, which is also confirmed by specific-heat measurements.
We observe two pairs of magnetically inequivalent phosphorus positions
resulting in a pronounced four-peak structure of the single crystal ${}^{31}$P
NMR spectra characteristic of an incommensurate helimagnetic ground state. We
revealed a spatial redistribution of local fields at the P sites caused by Fe
spin-reorientation transition in high fields and developed an effective
approach to account for it. We demonstrate that all observed ${}^{31}$P spectra
can be treated within a model of an isotropic helix of Fe magnetic moments in
the ($ab$)-plane with a phase shift of 36$^{\circ}$ and 176$^{\circ}$ between
Fe1-Fe3 (Fe2-Fe4) and Fe1-Fe2 (Fe3-Fe4) sites, respectively, in accordance with
the neutron scattering data.
