  The aim of this paper is to provide a measurement of the mass accretion rate
in a large, complete sample of objects in the core of the star forming region
Rho-Oph. The sample includes most of the objects (104 out of 111) with evidence
of a circumstellar disk from mid-infrared photometry; it covers a stellar mass
range from about 0.03 to 3 Msun and it is complete to a limiting mass of ~0.05
Msun. We used J and K-band spectra to derive the mass accretion rate of each
object from the intensity of the hydrogen recombination lines, Pab or Brg. For
comparison, we also obtained similar spectra of 35 diskless objects. The
results show that emission in these lines is only seen in stars with disks, and
can be used as an indicator of accretion. However, the converse does not hold,
as about 50% of our disk objects do not have detectable line emission. The
measured accretion rates show a strong correlation with the mass of the central
object (Macc ~ Mstar^1.8+-0.2) and a large spread, of two orders of magnitude
at least, for any interval of Mstar. A comparison with existing data for Taurus
shows that the objects in the two regions have similar behaviour, at least for
objects more massive than ~0.1Msun. The implications of these results are
briefly discussed.
