An experimental study of ${}^{258,260}$Sg produced in the complete fusion reactions ${}^{52,54}$Cr,+,${}^{207}$Pb was performed using the SHELS velocity filter. The prompt neutron multiplicities in the spontaneous fission of ${}^{258,260}$Sg were measured for the first time, yielding average values of $\bar{\nu }{(}^{258}\mathrm{\text{Sg}})=4.9\pm 0.4$ and $\bar{\nu }{(}^{260}\mathrm{\text{Sg}})=5.03\pm 0.14$. The $\alpha$-decay branching ratio of ${}^{260}$Sg was determined to be $b_{\alpha }=0.29\pm 0.03$. In addition, the half-lives were measured as $T_{1/2}{(}^{258}\mathrm{\text{Sg}})={2.2}_{-1.0}^{+2.4}$,ms (95% C.L., confidence limit) and $T_{1/2}{(}^{260}\mathrm{\text{Sg}})={7.0}_{-1.7}^{+2.6}$,ms (95% C.L.).