We estimated radiative efficiency, spin and supermassive black hole (SMBH) mass values for sample of 33 distant low luminosity active galactic nuclei (AGNs). The distribution of the estimated spin values (majority of objects have a spin greater than 0.8) is fairly typical for many types of AGNs. The dependence of the estimated spin values on the estimated SMBH masses shows strong correlation between them, which suggests a rapid increase in spin with mass, i.e., that the main mechanism of mass growth in this case is disk accretion. We did not find any significant qualitative differences in the spin characteristics between our objects and objects of other types considered in the paper.