Single-photon avalanche diodes (SPADs) in the CMOS technology are very attractive solution for photon detection due to the excellent timing resolution achievable. Unfortunately, such devices suffer from large values of the dark count (DC) pedestals. In this paper, we analyzed a test chip containing SPADs with different layouts, implemented in the 150-nm CMOS technology. The behavior of such devices has been investigated after proton irradiation. It is observed that, after irradiation, the DC rate switches between two or more discrete levels, phenomenon known as random telegraph signal (RTS). The effect is related to the density and distribution of defects in the semiconductor lattice. RTS characteristics have been studied as the function of both temperature and bias voltage. Discussion of results and main hypotheses on defect types responsible for RTS are reported.