  PICO bubble chambers have exceptional sensitivity to inelastic dark
matter-nucleus interactions due to a combination of their extended nuclear
recoil energy detection window from a few keV to $O$(100 keV) or more and the
use of iodine as a heavy target. Inelastic dark matter-nucleus scattering is
interesting for studying the properties of dark matter, where many theoretical
scenarios have been developed. This study reports the results of a search for
dark matter inelastic scattering with the PICO-60 bubble chambers. The analysis
reported here comprises physics runs from PICO-60 bubble chambers using
CF$_{3}$I and C$_{3}$F$_{8}$. The CF$_{3}$I run consisted of 36.8 kg of
CF$_{3}$I reaching an exposure of 3415 kg-day operating at thermodynamic
thresholds between 7 and 20 keV. The C$_{3}$F$_{8}$ runs consisted of 52 kg of
C$_{3}$F$_{8}$ reaching exposures of 1404 kg-day and 1167 kg-day running at
thermodynamic thresholds of 2.45 keV and 3.29 keV, respectively. The analysis
disfavors various scenarios, in a wide region of parameter space, that provide
a feasible explanation of the signal observed by DAMA, assuming an inelastic
interaction, considering that the PICO CF$_{3}$I bubble chamber used iodine as
the target material.
