  Let f be a CM modular form and p an odd prime which is inert in the CM field.
We construct two p-adic L-functions for the symmetric square of f, one of which
has the same interpolating properties as the one constructed by
Delbourgo-Dabrowski, whereas the second one has a similar interpolating
properties but corresponds to a different eigenvalue of the Frobenius. The
symmetry between these two p-adic L-functions allows us to define the plus and
minus p-adic L-functions \`a la Pollack. We also define the plus and minus
p-Selmer groups analogous to Kobayashi's Selmer groups. We explain how to
relate these two sets of objects via a main conjecture.
