  Surveys of young star-forming regions have discovered a growing population of
planetary-mass (<13 M_Jup) companions around young stars. There is an ongoing
debate as to whether these companions formed like planets (that is, from the
circumstellar disk), or if they represent the low-mass tail of the star
formation process. In this study we utilize high-resolution spectroscopy to
measure rotation rates of three young (2-300 Myr) planetary-mass companions and
combine these measurements with published rotation rates for two additional
companions to provide a look at the spin distribution of these objects. We
compare this distribution to complementary rotation rate measurements for six
brown dwarfs with masses <20 M_Jup, and show that these distributions are
indistinguishable. This suggests that either that these two populations formed
via the same mechanism, or that processes regulating rotation rates are
independent of formation mechanism. We find that rotation rates for both
populations are well below their break-up velocities and do not evolve
significantly during the first few hundred million years after the end of
accretion. This suggests that rotation rates are set during late stages of
accretion, possibly by interactions with a circumplanetary disk. This result
has important implications for our understanding of the processes regulating
the angular momentum evolution of young planetary-mass objects, and of the
physics of gas accretion and disk coupling in the planetary-mass regime.
