  We present the first search for spinning dust emission from a sample of 34
Galactic cold cores, performed using the CARMA interferometer. For each of our
cores we use photometric data from the Herschel Space Observatory to constrain
N_{H}, T_{d}, n_{H}, and G_{0}. By computing the mass of the cores and
comparing it to the Bonnor-Ebert mass, we determined that 29 of the 34 cores
are gravitationally unstable and undergoing collapse. In fact, we found that 6
cores are associated with at least one young stellar object, suggestive of
their proto-stellar nature. By investigating the physical conditions within
each core, we can shed light on the cm emission revealed (or not) by our CARMA
observations. Indeed, we find that only 3 of our cores have any significant
detectable cm emission. Using a spinning dust model, we predict the expected
level of spinning dust emission in each core and find that for all 34 cores,
the predicted level of emission is larger than the observed cm emission
constrained by the CARMA observations. Moreover, even in the cores for which we
do detect cm emission, we cannot, at this stage, discriminate between free-free
emission from young stellar objects and spinning dust emission. We emphasise
that, although the CARMA observations described in this analysis place
important constraints on the presence of spinning dust in cold, dense
environments, the source sample targeted by these observations is not
statistically representative of the entire population of Galactic cores.
