The phenomenon of chirality induced spin selectivity (CISS) has triggered significant activity in recent years, although many aspects of it remain to be understood. For example, most investigations are focused on spin polarizations collinear to the charge current, and hence longitudinal magnetoconductance (MC) is commonly studied in two-terminal transport experiments. Very little is known about the transverse spin components and transverse MC - their existence, as well as any dependence of this component on chirality. Furthermore, the measurement of the CISS effect via two-terminal MC experiments remains a controversial topic. Detection of this effect in the linear response regime is debated, with contradicting reports in the literature. Finally, the potential influence of the well-known electric magnetochiral effect on CISS remains unclear. To shed light on these issues, in this work we have investigated the bias dependence of the CISS effect using planar carbon nanotube networks functionalized with chiral molecules. We find that (a) transverse MC exists and exhibits tell-tale signs of the CISS effect, (b) transverse CISS MC vanishes in the linear response regime establishing the validity of Onsager's relation in two-terminal CISS systems, and finally (c) the CISS signal remains present even in the absence of electric magneto chiral effects, suggesting the existence of an alternative physical origin of CISS MC.