  We report ^{115}In nuclear magnetic resonance (NMR) measurements in the
heavy-fermion superconductor CeCoIn_5 as a function of temperature in different
magnetic fields applied parallel to the $(\hat a, \hat b)$ plane. The
measurements probe a part of the phase diagram in the vicinity of the
superconducting critical field H_{c2} where a possible inhomogeneous
superconducting state, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), is stabilized.
We have identified clear NMR signatures of two phase transitions occurring in
this part of the phase diagram. The first order phase transitions are
characterized by the sizable discontinuity of the shift. We find that a
continuous second order phase transition from the superconducting to the FFLO
state occurs at temperature below which the shift becomes temperature
independent. We have compiled the first phase diagram of CeCoIn_5 in the
vicinity of H_{c2} from NMR data and found that it is in agreement with the one
determined by thermodynamic measurements.
