  We present 6 cm Very Large Array observations of the Greene & Ho (2004)
sample of 19 low-mass active galaxies with high accretion rates. This is one of
the only studies of a uniform sample of narrow-line Seyfert 1 (NLS1) galaxies
with such high sensitivity and resolution. Although we detect only one source,
the entire sample is very radio-quiet down to strong limits. GH10 was found to
have a radio power of 8.5 x 10^21 W/Hz, and a ratio R = f(6 cm)/f(4400 A) of
2.8. The 3 sigma upper limits for the remaining nondetections correspond to
radio powers from 3 x 10^20 to 8 x 10^21 W/Hz and 0.47 < R <9.9. Stacking all
nondetections yields an even stronger upper limit of R < 0.27. An assessment of
existing observations in the literature confirms our finding that NLS1s are
consistently radio-quiet, with a radio-loud fraction of 0%-6%, which is
significantly lower than the 10%-20% observed in the general quasar population.
By analogy with stellar-mass black holes, we argue that AGNs undergo a state
transition at L_bol/L_Edd~0.01. Below this value a radiatively inefficient
accretion flow effectively drives an outflow, which disappears when the flow
turns into an optically thick, geometrically thin disk, or a radiation
pressure-dominated slim disk at still higher L_bol/L_Edd.
