Numerical simulations have shown that distributed micro-roughness (DMR) can delay laminar-turbulent transition and reduce drag in a Blasius boundary layer. This surface-based drag-reduction concept has practical engineering value, but its generality and the underlying mechanisms remain unclear. Here, we investigate DMR effects on transition and turbulent flow in a three-dimensional boundary layer using direct numerical simulation. The simulated three-dimensional boundary layer develops under a crossflow-inducing configuration, yielding a crossflow component. Three DMR geometries are considered: peak-valley (DMR), peak-only (DMR-P), and valley-only (DMR-V). The DMR effect is quantified using the decomposition of the friction coefficient via the Fukagata-Iwamoto-Kasagi (FIK) identity. The total friction distributions indicate that, relative to the smooth case, the transition location shifts downstream for DMR and DMR-V. In the turbulent region, all DMR cases yield a drag reduction of 1-4%. Therefore, drag reduction via DMR can occur not only in canonical Blasius boundary layers but also in complex systems such as three-dimensional boundary layers. Using the FIK identity together with flow-field analyses and turbulence statistics, we examine how DMR alters the transition process and turbulence dynamics, and we discuss the distinct roles of the peak-valley, peak-only, and valley-only geometries.