  The energy source powering the extreme optical luminosity of
hydrogen-stripped Superluminous Supernovae (SLSNe-I) is not known, but recent
studies have highlighted the case for a central engine. Radio and/or X-ray
observations are best placed to track the fastest ejecta and probe the presence
of outflows from a central engine. We compile all the published radio
observations of SLSNe-I to date and present three new observations of two new
SLSNe-I. None were detected. Through modeling the radio emission, we constrain
the sub-parsec environments and possible outflows in SLSNe-I. In this sample we
rule out on-axis collimated relativistic jets of the kind detected in Gamma-Ray
Bursts (GRBs). We constrain off-axis jets with opening angles of 5\arcdeg\
(30\arcdeg) to energies of $\rm{E_k<4\times10^{50}\,erg}$
($\rm{E_k<10^{50}\,erg}$) in environments shaped by progenitors with mass-loss
rates of $\dot{M}<10^{-4}\,M_{\odot}\,{\rm yr}^{-1}$
($\dot{M}<10^{-5}\,M_{\odot}\,{\rm yr}^{-1}$) for all off-axis angles, assuming
fiducial values $\epsilon_e=0.1$ and $\epsilon_B=0.01$. The deepest limits rule
out emission of the kind seen in faint un-collimated GRBs (with the exception
of GRB\,060218), and from relativistic supernovae. Finally, for the closest
SLSN-I SN 2017egm we constrained the energy of an uncollimated non-relativistic
outflow like those observed in normal SNe to $E_{\rm k}\lesssim10^{48}$ erg.
