  We have experimentally studied the electronic $3p-> 3s$ excitation of Na
atoms attached to $^3$He droplets by means of laser-induced fluorescence as
well as beam depletion spectroscopy. From the similarities of the spectra
(width/shift of absorption lines) with these of Na on $^4$He droplets, we
conclude that sodium atoms reside in a ``dimple'' on the droplet surface and
that superfluid-related effects are negligible. The experimental results are
supported by Density Functional calculations at zero temperature, which confirm
the surface location of Na, K and Rb atoms on $^3$He droplets. In the case of
Na, the calculated shift of the excitation spectra for the two isotopes is in
good agreement with the experimental data.
