We have carried out $^{63,65}$Cu NMR spectra measurements in magnetic field up to about 45~T on single crystal of a multiferroic triangular antiferromagnet CuCrO$_2$. The measurements were performed for magnetic fields aligned along the crystal $c$-axis. Field and temperature evolution of the spectral shape demonstrates a number of phase transitions. It was found that the 3D magnetic ordering takes place in the low field range ($Hlesssim15$~T). At higher fields magnetic structures form within individual triangular planes whereas the spin directions of the magnetic ions from neighboring planes are not correlated. It is established that the 2D-3D transition is hysteretic in field and temperature. Lineshape analysis reveals several possible magnetic structures existing within individual planes for different phases of CuCrO$_2$. Within certain regions on the magnetic H-T phase diagram of CuCrO$_2$ a 3D magnetic ordering with tensor order parameter is expected.
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