  The hyperfine constants of the $^3$P$^{\circ}_2$ state in neutral Yb have
been measured using three different dipole transitions. This state was recently
shown to have a comparatively large hyperfine magnetic octupole splitting, and
thus a puzzlingly large magnetic octupole moment. The measurement is performed
using collinear laser spectroscopy on a fast atomic beam, which provides a
straightforward route to probing long-lived metastable atomic states with high
resolution. From the combined analysis of all three lines we find no
significant evidence for a non-zero octupole moment in $^{173}$Yb.
