Nontrivial band topologies in semimetals lead to robust surface states that can contribute dominantly to the total conduction. This may result in reduced resistivity with decreasing feature size contrary to conventional metals, which may highly impact the semiconductor industry. Here we study the resistivity scaling of a representative topological semimetal CoSi using realistic band structures and Green's function methods. We show that there exists a critical thickness d_c dividing different scaling trends. Above d_c, when the defect density is low such that surface conduction dominates, resistivity reduces with decreasing thickness; when the defect density is high such that bulk conduction dominates, resistivity increases in as conventional metals. Below d_c, the persistent remnants of the surface states give rise to decreasing resistivity down to the ultrathin limit, unlike in topological insulators. The observed CoSi scaling can apply to broad classes of topological semimetals, providing guidelines for materials screening and engineering. Our study shows that topological semimetals bear the potential of overcoming the resistivity scaling challenges in back-end-of-line interconnect applications.