We estimate the optical depth, time-scale distribution and fraction of micr
olensing events originating from sources in the Sagittarius dwarf galaxy (S
gr) lensed by deflectors in the Milky Way. These evens have a time-scale lo
nger by a factor similar to1.3 than the MW/MW events and occur mainly on so
urces fainter than V similar to 21 mag below Sgr's turn off. The fraction o
f events involving a source in Sg depends on the location and extinction of
the field and on the limiting magnitude of the survey. The contribution of
the MW/Sgr events is negligible (less than or similar to1%) at very low la
titudes (\b\ less than or similar to2 degrees) but increases continuously t
owards higher \b\ and becomes dominant near the highest density region of t
he dwarf galaxy. Sgr is present within the fields of current microlensing s
urveys and any optical depth map inferred from observations will become bia
sed by the presence of Sgr towards higher \b\ where the contribution of MW/
Sgr events is significant. Systematic spectroscopic measurements on the sou
rces of all the microlensing events may allow detection of this kind of eve
nt for which the degeneracy on the lens mass can be significantly reduced.