We performed a set of non-contact measurements using scanning probe microscope at room temperature such as Kelvin probe measurements and measurements of local differential capacitance of single-walled carbon nanotubes (SWCNT) doped with CuI. SWCNT with essential deviated values of work function were observed with Kelvin probe measurements. Deviations of work function we attribute to the presence and of CuI impurities and their peculiarities of structure. Differential capacitance measurements demonstrated absence of the essential decrease of the conductivity because if of CuI dopant.