A general phenomenological method for studying a two-pion mass spectrum is developed; it is shown that, without assumptions about the production mechanism of the two-pion system, no significant upper limit on the $\omega \to {\pi }^{+}{\pi }^{-}$ branching ratio can be set with present-day experiments. In general, a lower limit may be set if a significant effect is seen. This method is applied to data containing more than $8000\omega \to {\pi }^{+}{\pi }^{-}{\pi }^0$ events. The lower-momentum half of the sample, which shows a significant $\omega \to {\pi }^{+}{\pi }^{-}$ signal, was published previously but is here reanalyzed to set a lower limit on the $\omega \to {\pi }^{+}{\pi }^{-}$ branching ratio. The new data at higher momenta show no significant $\omega \to {\pi }^{+}{\pi }^{-}$ signal. The results from the various momenta are shown to be consistent.