Macroscopic magnetization, muon spin rotation (µSR), and NMR measurements were carried out to study magnetism in the Na1CoO2 cobaltate. Using superconducting quantum interference device measurements, Na1CoO2 is shown to have a bulk magnetic susceptibility much lower and flatter than that of NaxCoO2 with x=0.7-0.9. In fact, µSR yields a signal of mostly nonmagnetic origin, which is attributed to the x=1 phase. The intrinsic cobalt spin susceptibility corresponding to this x=1 phase is measured using 23 Na NMR. It is indeed found to be almost zero, in agreement with a low-spin 3+ charge state of all cobalt atoms. This single state of Co ions in CoO2 planes is confirmed by 59 Co NMR, whose determination of cobalt shift and quadrupolar parameters allows us to give a reference value of the Co 3+ orbital shift in cobaltates.